Prove that : `2 sin^2 theta + 4 cos (theta + alpha) sin alpha sin theta + cos 2 (alpha + theta)` is independent of `theta.`

The expression nsin^(2) theta + 2 n cos( theta + alpha ) sin alpha sin theta + cos2(alpha + theta ) is independent of theta , the value of n is

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

Show that cos^2theta+cos^2(alpha+theta)-2cosalphacostheta"cos"(alpha+theta) is independent of thetadot

Prove that : (1+ sin theta - cos theta) / (1+ sin theta + cos theta ) = tan (theta/2)

Prove that : (cos 4theta + cos 3theta + cos 2theta)/(sin 4theta + sin 3theta + sin 2theta) = cot 3theta

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta

Prove that : (2 cos^(3) theta-cos theta)/(sin theta-2 sin^(3)theta)=cot theta

Prove that: sin4 theta=4 sin theta cos^(3)theta-4cos theta sin^(3)theta

Prove that : (sin^(2)theta)/(cos theta)+cos theta=sec theta

Prove that (cos theta+sin theta )^2 + (cos theta - sin theta )^2 =2