# How do I prove that 5 - 5cos^2 x = 5sin^2 x?

$L H S = 5 - 5 {\cos}^{2} x$
$= 5 \left(1 - {\cos}^{2} x\right) = 5 {\sin}^{2} x = R H S$
Note that ${\sin}^{2} x + {\cos}^{2} x = 1$