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: $cos^2x-sin^2x=1-2sin^2x$

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