Question #eaa93

1 Answer
Sep 27, 2017

We are using Following formulas to Prove this identity
1. cos^2x+sin^2x=1
2. a^2-b^2=(a+b)(a-b)

L.H.S.
cos^4x-sin^4x-2cos^2x
=(cos^2x)^2-(sin^2x)^2-2cos^2x
using a^2-b^2=(a+b)(a-b)
=(cos^2x-sin^2x)xx(cos^2x+sin^2x)-2cos^2x
=(cos^2x-sin^2x)xx(1)-2cos^2x
=cos^2x-sin^2x-2cos^2x
=-cos^2x-sin^2x
=-(cos^2x+sin^2x)
=-(1)=-1 = R.H.S.

HENCE PROVED