Question

Prove the identity.sin ²x-cos²x=2 sin ²x-1

Answer 1

we have the identity

$sin²x-cos²x=2sin²x-1$

Remember that

$\begin{gathered} sin^2x+cos^2x=1 \\ isolate\text{ cos}^2x \\ cos^2x=1-sin^2x \\ substitute\text{ in the original problem} \\ sin^2x-[1-sin^2x]=2sin^2x-1 \\ sin^2x-1+sin^2x=2sin^2x-1 \\ 2sin^2x-1=2sin^2x-1\text{ ----> is proved} \end{gathered}$