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]
2 years ago
6

How to prove this???

Mathematics
1 answer:
swat322 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
What is -19 equal to
Dennis_Churaev [7]

Answer:

-19

Step-by-step explanation:

4 0
2 years ago
Someone please help me
kifflom [539]
It's 4 ways 'cause u can travel by car, boat, train, and plane
6 0
2 years ago
darryl spent $276 on books. math books cost $21 and English books cost $30. if he bought a total of 11 books how many of each ki
nata0808 [166]
6 math books would be 126
5 English books would be 150
126+150=276 
6 0
3 years ago
Can someone tell me the answer please ?<br> ​
monitta

Answer:

130 degrees

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Ryan gets off the bus at 4: 09 PM. He rides the bus for 17 minutes to get home from school. At what time does Ryan get on the bu
Lady_Fox [76]
He gets on the bus at 3:52 PM.
6 0
3 years ago
Other questions:
  • A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
    8·1 answer
  • + 10<br>The perimeter of a square is 60cm.<br>Work out the area of the square,<br>cm2​
    14·2 answers
  • Find the area of the triangle below. Be sure to include the correct unit in your answer.
    10·1 answer
  • I WILL UPVOTE ALL ANSWERS
    13·1 answer
  • Find the product <br> 1. (x + 7) (X + 8)
    13·2 answers
  • A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is t
    12·2 answers
  • Brainliest? help please-
    14·2 answers
  • Please help me with this, But I can’t decide if it’s A or B. Please explain !!!
    15·2 answers
  • Determine the area A(-1,3) , B(-5,3), C (-5,3), D(-1,-2) 1 unit = 1 ft
    5·1 answer
  • Liam's baking plans changed. He
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!