Question #eaa93

1 Answer
Pankaj Solanki
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 **

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