Verified Answer :

caylus

Hello,

sin² x-cos² x=sin² x-(1-sin² x)=2sin² x-1
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Ckaranja

From the trigonometric identity: 

\(cos^{2}x + sin^{2} x\)=1
Making \(sin^{2}\)x the subject we get:
\(sin^{2}\)x=1-\(cos^{2}\)x
On evaluating the left hand side and replacing \(sin^{2}\)x with 1-\(cos^{2}\)x;
2(1-\(cos^{2}\)x)-1
This gives

=2-2\(cos^{2}x\)-1
=1-2\(cos^{2}\)x
From the identity in \(cos^{2}\)x+\(sin^{2}\)x=1, replace 1 in the equation to get;
\(cos^{2}\)x+\(sin^{2}\)x-2\(cos^{2}\)x
=\(sin^{2}\)2x-\(cos^{2}\)x

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