How do you verify #cos^2(x)-sin^2(x)=1-2sin^2(x)#?

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Answer 1 · 2018-06-11T05:37:35

Below

RTP: #cos^2x-sin^2x=1-2sin^2x#

LHS:
#cos^2x-sin^2x#

Recall: #cos^2x+sin^2x=1# so #cos^2x=1-sin^2x#
= #(1-sin^2x)-sin^2x#

=#1-sin^2x-sin^2x#

= #1-2sin^2x#

= RHS

Therefore: #cos^2x-sin^2x=1-2sin^2x#