(1 - cot theta) ^ 2 + (1 + cot theta) ^ 2 = 2cosec ^ 2 theta​

Answers

Answer 1

[tex]\text{L.H.S}\\\\=(1 - \cot \theta )^2 + (1 + \cot \theta)^2 \\\\=(1-\cot \theta + 1 + \cot \theta)^2 - 2(1 -\cot \theta)(1 + \cot \theta)\\\\=2^2 - 2(1 - \cot^2 \theta)\\\\=4-2+2 \cot ^2 \theta\\\\=2+2 \cot^2 \theta\\\\=2(1 + \cot^2 \theta)\\\\=2 \csc^2 \theta\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]


Related Questions

a. If the swimming pool is 4 feet deep, what is the approximate volume of the swimming pool?

Answers

Answer:

64 ft³

Step-by-step explanation:

given that l = 4 ft

Since a swimming pool is like a cube

:- V= l³

V = 4³

V = 64 ft³

A taxi charges a flat rate of $2.00, plus an additional $3 per mile. If Erica has at most $20 to spend on the cab ride, how far could she travel? Write an inequality and solve

Answers

Answer:

6 miles

Step-by-step explanation:

20.00 - 2.00 = 18

18/3 = 6

she can travel 6 miles

A square has an area of 81 square inches. What is its perimeter?

Answers

Area of square = [tex]s^2[/tex] where, [tex]s[/tex] is the side length of the square.

[tex]81=s^2[/tex]

[tex]9=s[/tex]

s must be positive since it is a side length, so the negative root of 81 is rejected.

Perimeter= [tex]4s[/tex]

Perimeter= [tex]4(9)=36inches[/tex]

Step-by-step explanation:

In order to find the perimeter we need to find the length first ...

...Here, the area is already given ...

Area = 81 inches square

length = ?

Now....

( The formula of area is l × l )

[tex]area = {l}^{2} [/tex]

[tex]81 = {l}^{2} [/tex]

Now we should find square root of 81...

[tex]l = \sqrt{81} [/tex]

[tex]l \: = 9[/tex]

Now we find length so it's easy for us to find perimeter...

The formula of perimeter of square is 4l ..

= 4l

= 4 × 9

= 36 inches

hence the answer is 36 inches....

Find the value of x in the parallelogram below.

Answers

Answer:

x = 25

y = 6

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

2x and 50 are opposite angles,

2x = 50

Divide 2 on both sides,

x = 50 / 2

x = 25

In a parallelogram opposite sides are equal.

y + 5 and 11 are opposite sides,

y + 5 = 11

y = 11 - 5

y = 6

Answer:

x=25

y=6

Step-by-step explanation:

from the diagram,

2x= 50(opposite angles of a parallelogram)

2x= 50

dividing bothsides by 2

2x/2=50/2

x= 25

then,

y+5=11(opposite sides of a parallelogram)

y= 11-5

y= 6

what is the value of...
4x - x + 5, when x = 3
???

Answers

Answer:

The value of 4x-x + 5 when x + 3 is 14

Step-by-step explanation:

4(3)= 12 - 3= 9 + 5= 14

The value of 4x - x + 5 when x = 3 is 14.

To find the value of 4x - x + 5 when x = 3, we substitute the value of x into the expression and simplify.

Plugging in x = 3, we have:

4(3) - 3 + 5

Now let's simplify each term:

4(3) = 12

-3 = -3

Now we can substitute the simplified terms back into the expression:

12 - 3 + 5

Next, we perform the addition and subtraction in order from left to right:

12 - 3 = 9

9 + 5 = 14

Therefore, the value of 4x - x + 5 when x = 3 is 14.

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Find the remainder when f(x) = 5x² + 4x² - 2x + 4 is divided by x + 1.​

Answers

Answer:

I hope this helps you........

Double tap to add title • AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC? A 1200 B w c D 85​

Answers

Answer:

Step-by-step explanation:

I need help finding the slope and what m =

Answers

Answer:

4/3

Step-by-step explanation:

slope = rise/run =  (y1-y2)/(x1-x2) =   4 / 3

What is the volume (in cubic units) of a cylinder with a radius of 5 units and a height of 8 units? Assume that π = 3.14 and round your answer to the nearest tenth when necessary.

Answers

Answer:

V = hpir^2 = 12(3.14)(3)^2 = 108(3.14) = 339.1

Step-by-step explanation:

if u answered on the same 1 move on

help me i dont get this

Answers

The two-way table that shows the joint and the marginal relative frequencies is:

            Aerobic          Anaerobic     Total

Male       0.48              0.63               0.55

Female   0.52             0.37               0.45

Total         1                    1                      1

How to make a two-way table from the frequency table?

The table is given as:

            Aerobic     Anaerobic

Male       88               104

Female  96                62

The column total are:

Aerobic = 88 + 96 = 184

Anaerobic = 104+ 62 = 166

So, we have:

            Aerobic                        Anaerobic

Male       88/184 = 0.48              104/166 = 0.63

Female  96/184 =  0.52             62/166 = 0.37

The total count of the table is

Total = 184 + 166 = 350

So, we have:

            Aerobic          Anaerobic     Total

Male       0.48              0.63              (88 + 104)/350 = 0.55

Female   0.52             0.37               (96 + 62)/350 = 0.45

Hence, the two-way table that shows the joint and the marginal relative frequencies is:

            Aerobic          Anaerobic     Total

Male       0.48              0.63               0.55

Female   0.52             0.37               0.45

Total         1                    1                      1

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Based on the number of males and females doing aerobic and anaerobic respiration, the relative and marginal frequencies can be shown as:

                           Aerobic                     Anaerobic                        Total

Male                     47.8%                          62.7%                            54.9%

Female                 52.2%                          37.3%                            45.1%

                            100%                             100%                             100%

What are the relative and marginal frequencies given?

The frequencies for males are:

Aerobic = 88 / (88 + 96)                                    Anaerobic = 104 / (104 + 62)

= 47.8%                                                                                 = 62.7%

For females:                      

Aerobic = 100% - 47.8%                                    Anaerobic = 100 - 62.7%

= 52.2%                                                                                 = 37.3%

Total males frequency:                                Total females
= (88 + 104) / (88 + 104 + 96 + 62)               = 100% - 54.9%

= 54.9%                                                          = 45.1%

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Which expressions are equivalent to the given expression?
√80
80²
☐ 4√10
160²
8√5
4√5

Answers

Answer:

4 root 5

Step-by-step explanation:

√80 = √ 16 X √5

√16 = 4

so 4√5

18) Find the sum of the odd integers between 104 and 60.

Answers

Answer:

1,804

Step-by-step explanation:

106 - 60 = 44

44/2 = 22

60 + 22 = 82

82*22 = 1,804

Find the Surface Area:

A) 200 in^2
B) 300 in^2
C) 500 in^2
D) 400 in^2

Answers

Answer: B

Step-by-step explanation:

The first three terms of a geometric sequence are as follows 80, 40, 20 what are the next 2 terms of the sequence

Answers

80 40 20 10 5

Step-by-step explanation: Divide 20 by 40 then 40 by 80 They all are divisible by .5so then times .5 to get the next terms

What is the approximate Volume of the cone below?

Answers

Answer:

B - 183 cm3

Step-by-step explanation:

volume of a cone is 1/3 x pi x r^2 x H

Answer:Your answer is going to be D

Step-by-step explanation:

                                         

1/3 x 3.14 x 10^2 x 7 =732.66

Ms. Wimbley surveyed the middle school and found out that 70 students want to go to sky zone for the end of the year field trip. This represents 14% of the middle school. How many students are in the middle school?

Answers

Answer:

500

Step-by-step explanation:

If 700 is 14%, then x=100%

We do:

700=14%

x=100%

Then, we cross multiply to get

14x=7000

We divide 14 on each side, and get x=7000/14 which is x=500

So there are 500 total students in the middle school

Hope this helped you! If the answer is wrong, please tell me and I will correct it. Also, I would appriceate if you gave me a Brainliest. It means a lot to me :D

What is 8,-6 over the x-axis 90 degrees

Answers

Answer:

(6,8)

Step-by-step explanation:

The rule for 90 degree rotation is (x,y)=(-y,x)

So the answer is (6,8)

-0.5 = - m/6=

First answer get to be brainliest! ​

Answers

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\textsf{\textbf{\underline{Given question:-}}}[/tex]

        -0.5=-m/6. what is m?

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

    ❖  First, multiply both sides by 6 to get rid of the fraction:-

 ▪︎ -0.5*6=-m/6*6

On the RHS, the 6's cancel:-

◆-0.5•6=-m

Multiply:-

➪  [tex]\it{-3=-m}[/tex]

Divide by -1 on both sides:-

 ➪ [tex]\it{3=m}[/tex]

❒So we conclude that the value of m is 3.

✥ Good luck with your studies. ✥

          - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

m = 3

Step-by-step explanation:

⇒ -0.5 = - m/6

Divide both sides by -1.

⇒ -0.5/-1 = -m/(6 × -1)

⇒ 0.5 = m/6

Multiply both sides by 6.

⇒ 0.5 × 6 = m/6 × 6

m = 3

What is the measure of each angle of a regular 13-gon if necessary round to the nearest tenth

Answers

[tex]\textit{sum of all interior angles in a regular polygon}\\\\ \theta n=180(n-2) ~~ \begin{cases} \theta =\stackrel{degrees}{angle}\\ n=\stackrel{side's}{number}\\[-0.5em] \hrulefill\\ n=13 \end{cases}\implies \theta (13)=180(13-2) \\\\\\ 13\theta =180(11)\implies 13\theta =1980\implies \theta =\cfrac{1980}{13}\implies \theta \approx 152.3^o[/tex]

I NEED HELP!!!!
[tex]3(7+7i)+i(7+7i)[/tex]

Thanks!:)​

Answers

Solve the equation:-

[tex]3(7 + 7i) + i(7 + 7i) \\take \: common \: (7 + 7i) \: out\\ (7 + 7i) (3 + i) \: is \: your \: answer [/tex]

Open the equation:-

[tex]3(7 + 7i) + i(7 + 7i) \\ 21 + 21i + 7i + 7 {i}^{2} \\ 7 {i}^{2} + 28i + 21 \: \: answer[/tex]

Find the arc length of an arc with a Central angle of 2π/3 radians and a radius of 6 units

Answers

Answer:

Step-by-step explanation:

3 x 5/6 = ? x 1/6

those are fractions btw and what number makes the equation true?
PLEASE NO LINKS

Answers

Answer:

15

Step-by-step explanation:

[tex]3 \times \frac{5}{6} = \frac{15}{6} = 15 \times \frac{1}{6} [/tex]

If a slice of pizza is 2 dollars and I have 15 dollars how many pieces of pizza can I get

Answers

7 slices of pizza and you will have 1 dollar left over

Find the remainder of (h4+ h² - 2) /(h+3).

Answers

Answer:

remainder is 88

Step-by-step explanation:

if

[tex]h = 3[/tex]

[tex]f( - 3) = { ( - 3)}^{4} + { (- 3)}^{2} - 2[/tex]

[tex]f( - 3) = 88[/tex]

which is the remainder

Sin(15) × cos(15) × cos(30)​

Answers

Answer:

0.2165 to the nearest ten thousandth.

Step-by-step explanation:

Sin(15) × cos(15) × cos(30)​

= 0.258819 * 0.965926 * 0.866025

= 0.216506

solve the equation by completing the square. x²+6x-4=0​

Answers

Answer:

x = √13 - 3

x = -√13 - 3

Step-by-step explanation:

Given :

x² + 6x - 4 = 0

Solving :

x² + 6x + 9 - 9 - 4 = 0 [Adding and subtracting 9](x + 3)² - 13 = 0 [Group the square term together](x + 3)² -13 + 13 = 0 + 13 [Add 13 on both sides]√(x + 3)² = √13 [Taking square root on both sides]x + 3 - 3 = ±√13 - 3 [Subtract 3 from both sides]x = ±√13 - 3

Solutions :

x = √13 - 3x = -√13 - 3

Which statement is true

Answers

Answer:

the answer is only 5

Step-by-step explanation:

Interest is compounded semianually. Find the amount in the account after the given time.

Answers

Answer:

$1,159.69

Step-by-step explanation:

Compound Interest Formula :

A = P (1 + r/n)^(nt)A = amount P = principalr = rate (in decimals)n = number of times compoundedt = number of years

Solving :

A = (1,000)(1 + 0.05/2)²⁽³⁾A = (1,000)(1.025)⁶A = (1,000)(1.15969342)A = $1,159.69

What is the product (1 – 6i) (-5 – 8i) ?
PLEASE HELP QUICK!!!!!f

Answers

Answer:

[tex]-53+22i[/tex]

Step-by-step explanation:

You can simply use the FOIL method, but keep in mind that [tex]i^2=-1[/tex]:

[tex](1-6i)(-5-8i)\\(1)(-5)+(1)(-8i)+(-6i)(-5)+(-6i)(-8i)\\-5-8i+30i+48i^2\\-5+22i+48(-1)\\-5+22i-48\\-53+22i[/tex]

100 POINTS SOMEONE PLEASE HELP

A fireman needs to get water to a second-floor fire. His ladder is 33 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest tenth of a degree and show all your work.

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 50°. Will the ladder be safe the way it is positioned? Explain.

Answers

Answer:

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned

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