If A+B+C=[tex]\pi[/tex] show that tan A + tan B +tan C = tan A.tan B.tan C

Answers

Answer 1

Answer:

[tex]a + b + c = \pi \\ = > c= \pi - a - b \\ < = > \tan(c) = \tan(\pi - a - b) = -\tan(a + b) [/tex]

Step-by-step explanation:

we have:

[tex] \tan(a) + \tan(b) + \tan(c) \\ = \tan(a) + \tan(b) - \tan(a + b) \\ = \tan( a) + \tan(b) - \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{ ( \tan(a) + \tan(b) ) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (1)[/tex]

we also have:

[tex] \tan(a) \tan(b) \tan(c) \\ = - \tan(a) \tan(b) \tan(a + b) \\ = \frac{ -(\tan( a ) + \tan(b) ) \tan(a) \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{( \tan(a) + \tan(b)) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (2)[/tex]

from (1)(2) => proven


Related Questions

Factor 4b2 - 5b - 6.

A) (2b + 3)(2b + 2)
B) (4b + 3)(b - 2)
C) 2(b + 6)(2b - 1)
D) (b - 6)(4b + 1)

Answers

Answer:

[tex]4b^2 - 5b - 6 = 4b^2 -8b + 3b - 6 = 4b(b -2 )+3(b-2) = (4b+3)(b-2)[/tex]

option B

The factor form for of given expression is [tex](4b+3)(b-2)[/tex].

What is a method of factorizing?

Quadratic factorization using splitting of middle term : In this method splitting of middle term in to two factors.

What is the factor of given expression?

The middle term of the given expression -5b can be split as 3b-8b.

On using this in the given expression we get,

[tex]4b^2-5b-6=4b^2+3b-8b-6[/tex]

Take common factor out from first two and last two terms,

[tex]b(4b+3)-2(4b+3)[/tex]

Take the common factor out.

[tex](4b+3)(b-2)[/tex]

Therefore, the factor form of given expression is [tex](4b+3)(b-2)[/tex].

Learn more:https://brainly.com/question/25829061

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How much interest would Ms. Saver earn at the end of 1 year if she placed $5000 in a
bank that paid 3% interest?
A $10.50
B. $15.00
C. $150.00
D. $1500.00

Answers

When in doubt pick c my friend

Jenny cut an apple into eight equal slices. She gave
of the apple to Kendall.
Which shows how much of the apple Jenny has left?

Answers

Answer:

what did percent or fraction did she give Kendall?

Step-by-step explanation:

Can someone just check and tell me if this is right. If it's not correct can you explain how to do it?

Answers

AnswerI think its crrect]

Step-by-step explanation:

Answer:

75°

Step-by-step explanation:

When a quadrilateral is incribed in a circle, opposite angles equal 180.

180-105=75

Examine the system of equations.

5x + 6y = 32

5x – 6y = 8

Which variable or variables will be eliminated when you add the system of equations?


Which equation results from adding the system of equations?

Answers

9514 1404 393

Answer:

y is eliminated10x = 40

Step-by-step explanation:

The coefficients of y are opposites. Adding opposites results in a sum of 0. The y-term will be eliminated by adding the equations.

The result of that addition is ...

  (5x +6y) +(5x -6y) = (32) +(8)

  10x = 40

The measure of the angles of a triangle are shown in the figure below. Solve for x

Answers

Step-by-step explanation:

x+39+90=180 ( sum of angle of triangle is 180)

x=61

Help PLZZ NO FILES PLZZ

Answers

Answer:

5 (B)

Step-by-step explanation:

Which graph represents the inequality y ≥ x + 3m​

Answers

Answer:

Pardon, ne

Step-by-step explanation:

Your mother has a new cell phone. It comes with 18 apps already installed. She only uses 2/3 of those apps. She downloaded 12 more apps that she uses frequently. Write an equation to represent the total number apps your mom uses.

Answers

Awnser: sge uses 24 apps
Step by step explanation: 18 divided by 3 = 6. 6+6=12. 12+12=24.
Have a great day! Hope this helps

Answer:

Step-by-step explanation:

The cell phone comes with 18 apps already installed, but she only uses 2/3 of the apps. Therefore, we need to find 2/3 of 18 to find the number of apps she uses. 2/3 * 18 = 12 apps she uses frequently. Outside of that, she downloads 12 more frequently used apps, so you add 12 to 12 to get 24 total apps that she uses.

However, the question asks for the equation to find the answer. So, the equation would be like:

18(2/3) + 12 = x

where x is representing the number of apps she uses.

help pls 70 points i will mark brainliest​

Answers

Answer:

B

Step-by-step explanation:

there is a picture on top

NO LINKS!!!!!
Disregarding the force of gravity, the maximum velocity v of a rocket is given by v = t ln M, where t is the velocity of the exhaust and M is the ratio of the mass of the rocket with fuel to its mass without fuel. A solid propellant rocket has an exhaust velocity of 2.5 kilometers per second. Find its mass ratio M.

Answers

Answer:

look at the photo

Step-by-step explanation:

Disregarding the force of gravity, the maximum velocity v of a rocket is given by v = t ln M, where t is the velocity of the exhaust and M is the ratio of the mass of the rocket with fuel to its mass without fuel. A solid propellant rocket has an exhaust velocity of 2.5 kilometers per second. Find its mass ratio M.

7.5 = 2.5 ln Mln M = 3m = e^3 = 20.08553692

Hope it will help you

There is an image below. Is ThIs CoRrEcT? If it's wrong, what is it?

Answers

y-axis
quadrant 2
quadrant 3

HELPPPP MEEEEE ITS 5 GRADE MATH IK HELP ME IM FAILING RN :(((((

Answers

Answer:

i think c

Step-by-step explanation:

Answer:

Gross income for an individual—also known as gross pay when it's on a paycheck—is the individual's total pay from their employer before taxes or other deductions. This includes income from all sources and is not limited to income received in cash; it also includes property or services received.

Net income- In business and accounting, net income is an entity's income minus cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.

I think its B

Step-by-step explanation:

Change the decimal 5.4 to a percent. [make sure you include the % sign in your answer]

Answers

Answer:

5.4 as a percent is 540%

Hope I helped! :)

Answer:

I think the answer is 525%

please help find the gradient :)

Answers

Answer:

gradient m = - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

y = - x - 3 ← is in slope- intercept form

with gradient m = - 1

Answer:

[tex]\rm Slope = -1[/tex]

Step-by-step explanation:

Given :-

A equation of line .[tex]\rm y = -x-3[/tex]

And we need to find out the gradient of the line. The gradient of the line is the " slope " of the line. The given equation is in slope Intercept Form , which is ,

Slope intercept form :-

[tex]\rm\implies y = mx + c [/tex]

Where m is the slope of the line and c is y intercept .

On comparing it to slope Intercept Form , we have ,

[tex]\implies \rm Slope (m) = (-1)[/tex]

Hence the gradient of the line is (-1) .

ed on exam
115. Which is the equation of a
quadratic function with x-intercepts
(-5,0) and (1,0)?
a. y = x2 - 4x - 5
b. y = x2 - 4x + 5
c. y = x2 + 4x - 5
d. y = x2 + 4x + 5

Answers

Answer:

I believe it is C, y= x^2 +4x -5

I need this in 1 min

Answers

Answer: 12

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

Opps I'm sorry I did that wrong. Im  so sorry

If Mr. Bisby wants to know the average of the grades on a test, what measure of central tendency would he be looking at?

(Spelling counts so make sure to spell it correctly)

Answers

Answer: The answer is mean.

Step-by-step explanation:

This measure of central tendency helps you figure out the average of data.

A group of students is painting a background piece for the school play. What is the area of the gray part of the background. Please help no links

Answers

Answer:

1324 in²

Step-by-step explanation:

Rectangle: 40x30=1200

Triangle: 1/2x10x30=150

1200+150=1350

Door: 3x6=18

Window: 2x4=8

18+8=26

1350-26=1324

Find the equation of the line. Use exact numbers
y= ?x+ ?

Answers

Answer:

y=3x+3

Step-by-step explanation:

slope is 3 because rise over run. Rise is 3 and run is 1. 3/1 is 3. and b= y-intercept and the poiunt wehre the line intercepts the y axis is 3. so your answer is y=3x+3

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

what is x / 15 equals 5. what is x?​

Answers

Answer:

x = 75

Step-by-step explanation:

x/15 = 5

Multiply each side by 15

15*x/15 = 5*15

x = 75

Answer:

x = 75

Step-by-step explanation:

Reverse the problem meaning you have to do multiplication

5 times 15 is 75

To check your work divided 75 by 15 and if it equals 5 it is correct

Hope this helped :]


Meng had 346 stickers. On Monday he gave away 38. On Tuesday he gave away 49. on Wednesday he gave away 16.
How many stickers does Meng have left?

Answers

Answer:

243 stickers

Step-by-step explanation:

346-38=308

308-49= 259

259-16=243

Combine like terms to create an expression equivalent to: n +n + n + y + y

Answers

Answer:

[tex]3n+2y[/tex]

Step-by-step explanation:

LIKE TERMS: TERMS WHOSE VARIABLES AND EXPONENTS ARE THE SAME.

[tex](1)n+(1)n+(1)n+(1)y+(1)y[/tex]

When combining variables that do not have coefficients, there is always an invisible '1' in front of the variable.

[tex](1)n+(1)n+(1)n = 3n.[/tex]

[tex](1)y+(1)y=2y.[/tex]

[tex]3n+2y.[/tex]

If y varies directly as x and y = 24 when
x= 16, what is y when x = 50?

Answers

Answer:

[tex]y = 75[/tex]

Step-by-step explanation:

Given

[tex]y\ \alpha\ \ x[/tex]

[tex]y=24; x =16[/tex]

Required

Find y when [tex]x = 50[/tex]

We have:

[tex]y\ \alpha\ \ x[/tex]

Express as equation

[tex]y = kx[/tex]

Solve for k

[tex]k = \frac{y}{x}[/tex]

When [tex]y=24; x =16[/tex]

[tex]k = \frac{24}{16}[/tex]

[tex]k = \frac{3}{2}[/tex]

When [tex]x = 50[/tex], we have:

[tex]y = kx[/tex]

[tex]y = \frac{3}{2} * 50[/tex]

[tex]y = 75[/tex]

Help within 10 min pleeeeeeeeeease

Answers

The answer should be 75

Answer:

10

Step-by-step explanation:

HELP I WILL MARK BRAINLIEST

Answers

Answer:

308

Step-by-step explanation:

22 x 15.4 = 338.8

338.8 / 1.1 = 308

Help solve this problem pls

Answers

Not so clear to answer this

I am an arc that measures between Oº and 180° WHAT AM I?​

Answers

Answer:

a semicircle?

Step-by-step explanation:

Help !!!!!!!!!!!!!!!!!!!!!

Answers

[tex]\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}[/tex]

2

1+3

1+32+2

Thanks Thanks Hope it helps

Answer:

1+3=4

2+2=4

there are only 2 possible ways in which the sum will add up to 4

therefore the answer is 2

Simplify -4(2x - 3) + 7 x – 1.​

Answers

Answer:

-x+11

Step-by-step explanation:

The answer is -x+11
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