# How do you prove Sin^2-cos^2=2sin^2-1 ?

Replace in the equation ${\cos}^{2} x$ by $\left(1 - {\sin}^{2} x\right)$
${\sin}^{2} x + {\cos}^{2} x = 1 \text{ "=>" } {\cos}^{2} x = 1 - {\sin}^{2} x$
${\sin}^{2} x - \left(1 - {\sin}^{2} x\right) = 2 {\sin}^{2} x - 1.$