Question

@ganeshie8
Need help with Tricky Trig identity question. Question is in attached file

Answer 1

Hint :
\[2\cos^2x = 1 + \cos(2x)\]

Answer 2

this is going to take a while

Answer 3

\[8\cos^4x = 2 (2\cos^2x)^2 = 2(1+\cos(2x))^2\]

Answer 4

\[ = 2(1+2\cos(2x) + \cos^2(2x))\]

\[ = 2+4\cos(2x) + 2\cos^2(2x)\]

Answer 5

how do i get the cos4x part?

Answer 6

apply the identity again

\[=2+4\cos(2x) + 1+\cos(4x)\]

\[=3+4\cos(2x) +\cos(4x)\]

Answer 7

ok so are we allowed to add the angle from (cos2x+1)+(cos2x+1)?

Answer 8

oh wait i see now. cos^2(2x)=cos4x. The angles have a ratio of 1:2