Question

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

Answer 1

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

Answer 2

Hello,

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