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
diamong [38]
3 years ago
6

How to prove this???

Mathematics
1 answer:
swat323 years ago
4 0
\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3)  \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 


go to right side now

4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)

use x^3 - y^3 = (x-y)(x^2 + xy + y^2) and x^3 + y^3 = x^2 - xy + y^2

4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow  4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad  \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)

so \sin^2 A + \cos^2 A = 1

4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side
You might be interested in
Work out the area of a circle in terms of pie when the radius is 6mm
FinnZ [79.3K]

Answer:

36π mm²

Step-by-step explanation:

Please, Mark, it's π or pi, not pie.  

Formula for the area of a circle:  A = πr²

so, if the radius is 6 mm, the area is A  =π(6 mm)² = 36π mm²

7 0
3 years ago
If you eat one quarter of a pizza and your dog eats one eighth of it, what percent is left over?
slamgirl [31]
Take 3 quarters minus one eighth and you’ll get ur answer
4 0
3 years ago
Needing help stuck on this.
Verdich [7]

Answer:

71

Step-by-step explanat

3 0
3 years ago
Look at the picture please help
morpeh [17]

Answer:

c

Step-by-step explanation:

First off, we know that (g ° f)(2) is just both functions done in a ordered fashion. In this case, f(x) is done first.

To figure out what f(2) is, all we have to do is find where x = 2 is on the graph. In this case it is on point (2, 3). The input is the x and the output is the y, so f(2) = 3.

Then, we can figure out what g(3) by locating x = 3 on line g. It shows the point (3, 0). This means that g(3) = 0.

3 0
2 years ago
A circle has a radius of 7 inches. What is the area of the circle?<br> Mark only one oval
Vikki [24]

Answer:A≈153.94in²

Step-by-step explanation:Hope this was helpful

3 0
3 years ago
Other questions:
  • How to factor 5x^2 +4x -1
    7·1 answer
  • Evaluate z+z+z for x =2,y=-3,z=4​
    14·1 answer
  • What are the diminshens of a cube with the volume of 216?
    5·1 answer
  • The population of a local species of beetle can be found using an infinite geometric series a1=960 and the common ratio is .25 w
    5·2 answers
  • There were 718 tickets purchased for a major league baseball game. The lower reserved tickets cost ​$9.50 and the upper reserved
    14·1 answer
  • No, the answer isn't 200. <br><br> Please explain.
    5·1 answer
  • Nikola buys a bouquet of
    7·1 answer
  • 2-3/4z=1/8z+9 please show your steps!
    7·1 answer
  • Suppose f(x) = 2x + 3. Find f(-.5).
    11·1 answer
  • Help me with this please!!!!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!