Question

state the half - angle identities used to integrate sin²x and cos²x. the half - angle formulas are sin²x = and cos²x =

Explanation:

Step1: Recall half - angle identity for $\sin^{2}x$

The double - angle formula for $\cos(2x)=1 - 2\sin^{2}x$. Solving for $\sin^{2}x$ gives $\sin^{2}x=\frac{1-\cos(2x)}{2}$.

Step2: Recall half - angle identity for $\cos^{2}x$

The double - angle formula for $\cos(2x)=2\cos^{2}x - 1$. Solving for $\cos^{2}x$ gives $\cos^{2}x=\frac{1 + \cos(2x)}{2}$.

Answer:

$\sin^{2}x=\frac{1-\cos(2x)}{2}$, $\cos^{2}x=\frac{1 + \cos(2x)}{2}$