1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wolverine [178]
3 years ago
9

I need to get the left side to equal the right side. Keeping the right side alone and not changing it.

Mathematics
1 answer:
likoan [24]3 years ago
7 0

<u>To prove the trigonometric equation:</u>

\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)

RHS=(\sin x+\cos x)(1-\sin x \cos x)

We know that \sin^2x +\cos^2x=1, substitute this in place of 1.

       =(\sin x+\cos x)(\sin^2x +\cos^2x-\sin x \cos x)

Multiply each term of the first term with each term of the 2nd term.

       =\sin^3x + \sin x \cos^2x-\sin^2 x \cos x+\cos x \sin^2 x + \cos^3 x-\sin x\cos^2 x

Group like terms together.

       =\sin^3x +( \sin x \cos^2x-\sin x\cos^2 x)+(\cos x \sin^2 x-\sin^2 x \cos x) + \cos^3 x

       =\sin^3x +( 0)+(0) + \cos^3 x

       =\sin^3x + \cos^3 x

       = LHS

RHS = LHS

\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)

Hence proved.

You might be interested in
[98 POINTS]<br><br> Explain how you would calculate the volume of the figure shown.<br> Be detailed.
N76 [4]

Answer:

1282.81824016

Step-by-step explanation:

Find the volume of the cone (the formula is π×r²×h/3) and the volume is 359.19

Now find the volume of the cylinder which is 923.6282401554 and we just add them together which is 1282.81824016

8 0
3 years ago
Read 2 more answers
The table shows the number of boys and girls who signed up for certain summer classes.
Makovka662 [10]

Answer:

Music and Dance

Step-by-step explanation:

When looking at the numbers for each class u want to add up the numbers. When u get the answers look for the two numbers witch are the closes to each other.

7 0
2 years ago
Can someone help me on this?
vlada-n [284]

Answer:

the triangle PQR is similar to RTS

Step-by-step explanation:

QR : RT

2 : 6

this 1:3 ratio is also seen in PR (4) with RS (12)

8 0
3 years ago
What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?
Gemiola [76]

Answer:

4x + 3y + 9 = 0

Step-by-step explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

                      $ (y - y_1) = m (x - x_1) $

where $m$ is the slope of the line and

           $ (x_1, y_1) $ is the point passing through it.

Here, $ m = \frac{-4}{3} $ and $ (x_1 , y_1) = (3 , -7) $.

Substituting in the formula y +  7 = \frac{-4}{3} (x - 3)

$ \implies 3y + 21 = -4x + 12 $

$ 4x + 3y + 9 = 0 $

3 0
3 years ago
lauramakes a 10.5% commison on each of her sales. how much does she make when she sells a house for 85,000?
loris [4]

Answer:    $8929


Step-by-step explanation:


5 0
3 years ago
Other questions:
  • What is the distance between points (12, 4) and (12, –10) on the coordinate plane?
    7·2 answers
  • Please help I will mark brainliest if correct.
    11·2 answers
  • How do i solve this equation? and could you show it to me step by step?
    14·1 answer
  • The sum of three integers is 92. The second number is three times the first number. The third number is ten less than twice the
    7·2 answers
  • Use a property of exponents to simplify. 3Use as the base.
    5·1 answer
  • The measure of an interior angle of a regular polygon is 174. Find the number of sides in the polygon.
    13·1 answer
  • WILL MARK BRAINLIEST!!!
    5·1 answer
  • What is 11k+9=42 ? and how to do the work for it
    11·2 answers
  • Please help I don't understand!
    9·1 answer
  • : David has saved $35 of the $140 he needs to purchase a new
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!