Question c38f4

Oct 24, 2016

Substitute in ${\cos}^{2} \left(x\right) = 1 - {\sin}^{2} \left(x\right)$.

Explanation:

Using the identity

${\sin}^{2} \left(x\right) + {\cos}^{2} \left(x\right) = 1$

we can subtract ${\sin}^{2} \left(x\right)$ from both sides to obtain

${\cos}^{2} \left(x\right) = 1 - {\sin}^{2} \left(x\right)$.

With that:

cos^2(x) - sin^2(x) = (1-sin^2(x))-sin^2(x))#

$= 1 - 2 {\sin}^{2} \left(x\right)$