Simplify csc θ(1−cos^2 θ)/sinθ cos θ to a single trigonometric function

Answers

Answer 1

Answer:

[tex]\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha[/tex]

Step-by-step explanation:

Step(i):-

Given that the trigonometric function

            [tex]\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha }[/tex]

  we know that    sin²∝ + cos²∝ = 1

                      ⇒    sin²∝ = 1- cos²∝

Now we have to simplify the given trigonometric function

                =       [tex]\frac{cosec\alpha(sin^{2} \alpha ) }{sin\alpha cos\alpha }[/tex]

               =       [tex]\frac{cosec\alpha(sin \alpha ) }{ cos\alpha }[/tex]

Step(ii)

         we know that  cosec∝ = 1/ sin∝

              = [tex]\frac{\frac{1}{sin\alpha } (sin \alpha ) }{ cos\alpha }[/tex]

    After cancellation sine function, we get

          =  [tex]\frac{1 }{ cos\alpha } = sec\alpha[/tex]

Final answer:-

[tex]\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha[/tex]

           

     

 

               


Related Questions

what is the real answer to infinity+infinity

Answers

Answer:

infinity

Step-by-step explanation:

Answer:

2(infinity) or 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

The list of ordered pairs is a function. which of the following to be the missing ordered pair? (12,6) (3,1) (2,-2) (5,10) (-8, -4) (___,___)

Answers

Answer:

D

Step-by-step explanation:

the awnser is D

Answer:

8,8

Step-by-step explanation:

Pls help extra points and mark brainlist

Answers

the answer is 29.Just solved it with pdas

Step-by-step explanation:

that seems like a decimal? 2.8?

9+6²-2.8

9+36-2.8

42.2

hope it helps.

have a great day :)

Any method to solve the quadratic equetion below over the set of complex numbers.

2x(x+6)=(x-4)(x+3)

Answers

The answer for this would be 55 good luck

Use your knowledge of special right triangles to find y. Write your answer in simplest radical form.

Please be quick

Answers

Answer:

[tex] \sin(30°) = \frac{10}{y} \\ \frac{1}{2} = \frac{10}{y} \\ \boxed{y = 20 \: mi}[/tex]

or,

[tex] \cos(60°) = \frac{10}{y} \\ \frac{1}{2} = \frac{10}{y} \\ \boxed{y = 20 \: mi}[/tex]

20 mi is the right answer.

HELP HELP!! WILL MARK BRAINILEST!!

Answers

Answer:

A

Step-by-step explanation:

can you please mark me brainlest :D

You roll a six sided die . What is the probability that the value of the roll will be a two or six ?

Answers

Answer:

2 out of 6

Step-by-step explanation:

I think its this because out of the 6 sides you are hoping that two of the outcomes are true

Help me! Which is the right correct answer?

Answers

Answer:

the way bottom one i think i dont rember planes anymore

Step-by-step explanation:

Answer:

(-4 1/2,3) is the final result.

Step-by-step explanation:

V(4 1/2, -3)

The order of the reflections do not matter.

So if I consider the x axis first, only the y value will change. Seems weird, but try doing this on a piece of scrap paper.

(4 1/2, 3 ) is the new point. The point is reflected an equal distance behind the mirror on the x axis.

Now do the y axis. Only the x value of the point is changed.

(-4 1/2, 3) is what happens.

===================================

Does the order matter?

V(4 1/2, - 3) goes across the y axis to become (-4 1/2 , - 3)

V'(-4 1/2, -3) goes across the x axis to become (-4 1/2, 3) which is exactly what we got before.

Order does not matter for these 2 transformations.

Which equation is a linear function?
y= 2 + 3
y = 22 - 1
y= 22 +7

Answers

Y=22+7 is the answer

need help asap please

Answers

Answer:

16°

Step-by-step explanation:

We know that in parallelogram opposite angles are equal so

4u - 8° = 6u - 40°

6u - 4u = 40° - 8°

2u = 32°

u = 32° /2

u = 16°

The value of u should be 16° to make PQRS parallelogram.

Hope it will help.

Answer:

[tex]\displaystyle 16 = u[/tex]

Step-by-step explanation:

Diagonal, opposite angles are congruent in every parallelogram:

[tex]\displaystyle [5u + 44]° = [14u - 100]° → -144 = -9u; 16 = u \\ \\ AND/OR \\ \\ [6u - 40]° = [4u - 8]° → -32 = -2u; 16 = u[/tex]

No matter which pair you take, you will ALWAYS arrive at the same exact solution.

I am joyous to assist you at any time.

HELP ME PLS stock worth $60 a share dropped in value by 20% on Monday. Then it dropped again by 10$ the next Tuesday. And finally increased by 55% the following Friday. What was the final price of a share?

Answers

Answer:

58.90

Step-by-step explanation:

What is the value of 6x - 3y if x = 5 and y = -1?
F. 11

G. 33

H. 65

I. 65

Answers

Answer:

G. 33

Step-by-step explanation:

[tex]6x - 3y \\ 6(5) - 3( - 1) \\ 30 + 3 \\ 33[/tex]

6x-3y

Now, if x = 5 and y = -1

6(5) -3(-1)

= 30+3

= 33

Which of the following problems would NOT have a solution?

Pablo has 30 pieces of candy and wants to divide them into 6 equal piles. You want to know how many pieces will be in each pile.

Pablo has 6 pieces of candy and wants to divide them into 4 equal piles. You want to know how many pieces will be in each pile.

Pablo has 0 pieces of candy and wants to divide them into 6 equal piles. You want to know how many pieces will be in each pile.

Pablo has 6 pieces of candy and wants to divide them into 0 equal piles. You want to know how many pieces will be in each pile.

Answers

Answer:

the last scenario

Step-by-step explanation:

you cannot divide anything by zero -- it's considered to be undefined

If 0 = 35, then solve for X.
X
9
Round to the nearest hundredth.

Answers

Answer:

x = 15.69

Step-by-step explanation:

Given that,

Height, h = 9

Hypotenuse, H = x

Angle, [tex]\theta=35[/tex]

We need to find the value of x.

The relation between height, Hypotenuse and the angle is given by :

[tex]\sin\theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\sin(35)=\dfrac{9}{x}\\\\x=\dfrac{9}{\sin(35)}\\\\x=15.69[/tex]

So, the value of x is 15.69.

The factory makes 400 cars per day. If the workday is eight hours long. What is the hourly rate at which car are produced

Answers

Answer:

50

Step-by-step explanation:

400/8 =50

Please solve if so thank you so much!!

Answers

Answer:

60 x 4

Step-by-step explanation:

Answer:

y=35x+60

x=4

Step-by-step explanation:

A planner assembles party favor bags filled with glow sticks and temporary tattoos for a client. There are 24 glow sticks and 30 temporary tattoos to divide evenly among the bags.

If there are no leftover items, what is the greatest number of bags the planner can assemble

Answers

Answer: The greatest number of bags is 6.

Step-by-step explanation:

In each bag, there would be 4 glow sticks and 5 tattoos, which is the greatest number that can be put in each bag without having any left.

112 yards
R
Sand
15 yards
Trap
20 yards s
If RS is parallel to AB, what is the width of the sand trap?
149 yards
82 yards
107 yards
84 yards

Answers

Answer:

my teacher has cancer please help her at #snowmanchallenge

Step-by-step explanation:

try to spread the help every snowman is ten dollars for her

Answer:

84

Step-by-step explanation:

112/20= 5.6

5.6*15=84

brainly is easy

There are 4 boys eating oranges. Each boy eats 1 / 2 of an orange. How many oranges did the boys eat?

Answers

Answer:

2 oranges

Step-by-step explanation:

Two halves make a whole orange, and since there's four of them, they are eating 2 oranges.

Answer:they would have eaten 2 because 1/2+1/2 is a whole and since there are 4 boys eating 1/2 of an orange they would have eaten 2 oranges

The price of a stock decreased $2 each day for seven consecutive days what was the total change in value of the stock over the seven days

Answers

Answer:

The stock lost $14 in 7 days

Step-by-step explanation: I know how to multiply.

The total change in the value of the stock over the seven days is $14 if the price of a stock decreased $2 each day for seven consecutive days.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that are +, -, ×, and ÷.

It is given that:

The price of a stock by decreased $2 each day for seven consecutive days

The price of a stock decreased by $2 per day for seven consecutive days.

Each day the cost is decreased by $2

Therefore, in 7 days the total reduction in cost is: 7×2= $ 14

So, the total change in the value of the stock is:  -$ 14.

The total change in the value of the stock over the seven-day period is:

It decreased by $ 14

Thus, the total change in the value of the stock over the seven days is $14 if the price of a stock decreased $2 each day for seven consecutive days.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Ten more than 2 times a number, n, is 16. What is the value of n?

A.
3

B.
–13

C.
–3

D.
13

Answers

Answer:

A

Step-by-step explanation:

Turn into equation

2n+10=16

Subtract 10 from both sides

2n=6

Divide by 2 from both sides

n=3

Which of the following expressions has the greatest value?
110
33
52
25

Answers

Answer:

2^5

,,,,,,,,,,, ,,,,,,,,,

Kendrick walked of a mile in of an hour. How fast did he walk? _____miles per hour​

Answers

Answer:

He walked at 1 mile per hour

Step-by-step explanation:

Answer:

He walked at 1 mph

Step-by-step explanation:

Simplify this expression.
6x + 3 – 4x + 2y + 7

Answers

Answer:

2x + 10 + 2y

Step-by-step explanation:

6x + 3 – 4x + 2y + 7

(6x - 4x) = 2x

2x + 3 +2y + 7

(3 + 7) = 10

Answer: 2x + 10 + 2y

Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins,
Alan uses 5 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 3 cup of oil and 1 egg. Alan has 4 cups of
oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan
wants to maximize the money raised at the bake sale. Let x represent the number of trays of blueberry muffins and
y represent the number of trays of bran muffins Alan bakes.
What are the constraints for the problem?

Answers

Answer:

1/3x + 1/2y < or equal to 12

2x + y < or equal to 12

x > or equal to 0

y > or equal to 0

1/3x + 1/2y < or equal to 4

Step-by-step explanation:

none

Answer:

A on edge :)

Step-by-step explanation:

edge2021

10% of ________ is 7
25% of ________ is 6

Answers

Answer:

I got

10% of 70 is 7

Answer:

First one is 70

Second one is 24

Step-by-step explanation:

First one :7*100=700

700÷10=70

The second one :6*100=600

600÷25=24

can anyone please help with this???

Answers

Answer:

car is decelerating

Step-by-step explanation:

solve the questions bellow

Answers

Answer:

1. 29.67°

2. 68.96°

3. 89.85°

Step-by-step explanation:

1. Reference angle = x

Opposite = 45 cm

Adjacent = 79 cm

Therefore:

[tex] tan(x) = \frac{45}{79} [/tex]

[tex] tan(x) = 0.569620253 [/tex]

[tex] x = tan^{-1}(0.569620253) [/tex]

[tex] x = 29.67 [/tex] (nearest hundredth)

2. Reference angle = B

Opposite = 14

Hypotenuse = 15

Therefore:

[tex] sin(B) = \frac{14}{15} [/tex]

[tex] sin(B) = 0.93333 [/tex]

[tex] B = sin^{-1}(0.93333) [/tex]

[tex] B = 68.96 [/tex] (nearest hundredth)

3. Reference angle = x

Adjacent = 238,900 mi

Hypotenuse = 92,955,807 mi

Therefore:

[tex] cos(x) = \frac{238,900}{92,955,807} [/tex]

[tex] x = cos^{-1}(\frac{238,900}{92,955,807}) [/tex]

[tex] x = 89.85 [/tex] (nearest hundredth)

Suppose that a chemist is mixing two acid​ solutions, one of 15​% concentration and the other of 25​% concentration. Which of the following concentrations could not be​ obtained?

Choose the correct answer below.

Answers

Answer: d. 29%

Step-by-step explanation:

The mixture of the two concentrations should equal a concentration that is between the concentration percentages of the two solutions.

This is because the lower concentration percentage will pull the higher one down while the higher concentration will pull the lower one up. It will not be possible to get a mixture concentration that is lower than the lower concentrated acid or higher than the higher concentration acid.

Mixture concentration must be between 15% and 25%.

Option D at 29% is therefore not possible.

A blueprint uses a scale factor of 3 inches = 2 feet. What is the area on the blueprint of a 3,500 square foot house in inches?

Answers

Answer:

7875 square inches

Step-by-step explanation:

4ft^2 = 2ft * 2ft

4ft^2 = 3in * 3in

4ft^2 = 9in^2

For 3,500 square foot

3,500 square foot  = x

Divide bith expressions

4/3500 = 9/x

4x = 9 * 3500

4x = 31500

x = 31500/4

x = 7875 square inches

Hence the area of the house in inches is 7875 square inches

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