Question

Prove the identity 2sin^2x - 1 = sin^2x - cos^2x

Answer 1

Hello,

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

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