If $ heta$ is any angle, then $\sin ^2 heta \cos ^2 heta=$

Question

If $	heta$ is any angle, then $\sin ^2 	heta \cos ^2 	heta=$

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Here, } \sin ^2 	heta \cos ^2 	heta \ & =\left(\frac{1-\cos 2 	heta}{2}ight)\left(\frac{1+\cos 2 	heta}{2}ight) \ & =\frac{1-\cos ^2 2 	heta}{4}=\frac{1-\left(\frac{1+\cos 4 	heta}{2}ight)}{4} \ & =\frac{1-\frac{1}{2}-\frac{\cos 4 	heta}{2}}{4}=\frac{1}{8}(1-\cos 4 	heta)\end{aligned}$

If $\theta$ is any angle, then $\sin ^2 \theta \cos ^2 \theta=$

Solution