Prove this identity!

Question

0

576

2

cos⁴x - sin⁴x = cos2x

No idea what to do here pls help!!!

Guest Dec 9, 2016

edited by Guest Dec 9, 2016
edited by Guest Dec 9, 2016

Alan · Answer 1 · 2016-12-09T02:01:36

cos⁴x - sin⁴x → (cos²x + sin²x)(cos²x - sin²x) → 1*(cos²x - sin²x) → cos(2x)

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Guest · Answer 2 · 2016-12-09T02:06:57

cos²x=1-sin²x

cos⁴x=(1-sin²x)²=1+sin⁴x-2sin²x

cos⁴x-sin⁴x=1+sin⁴x-2sin²x-sin⁴x=1-2sin²x=cos(2x)

cos(2x)=1-2sin²x is a trigonometric identity, you should know it.

but incase you dont know it, ill give you another one that will help you in the future:

cos(a+b)=cosa*cosb-sina*sinb