Posted by **sierra** on Monday, April 23, 2007 at 1:16pm.

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

Nasty one!

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:

R.S.

= cos 4x + 4cos 2x + 3

= 8cos^4 x – 8cos^2 x + 1 + 8cos^2 x – 4 + 3

= 8cos^4 x

= Left Side

!!!!!!!WOW!!!!!!

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