posted by sierra on .
Need help solving problems using the Trigonometric Identities: 8cos^4 thet=cos4theta+4cos2theta+3
I am a bit unsure how to solve it. I am aware that the first step I must take is to simplify the problem and then use the Product to Sum formula
let's start on the right side.
I will work on each term to make typing easier.
recall that cos 2A = 2cos^2 A - 1
I will use x for theta
cos 4x = 2cos^2 2x - 1
= 2(cos2x)(cos2x) - 1
=2[(2cos^2 x - 1)(2cos^2 x - 1)] - 1.
=2[(4cos^4 x - 4cos^2 x + 1) – 1
=8cos^4 x – 8cos^2 x + 1
4cos 2x = 4(2cos^2 x – 1)
= 8cos^2 x – 4
Now putting it all together:
= cos 4x + 4cos 2x + 3
= 8cos^4 x – 8cos^2 x + 1 + 8cos^2 x – 4 + 3
= 8cos^4 x
= Left Side