Simplify: `(asin theta +b cos theta)^2 +(acos theta - bsin theta)^2`

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

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

If tan theta=a/b then b cos 2theta+asin 2theta=

Find the maximum and minimum values of the following expressions (i) a cos theta - bsin theta (ii) 7 cos theta + 24 sin theta

If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

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

(sin theta + sin 2 theta)/( 1 + cos theta + cos 2 theta) = tan theta.

If cos theta + sin theta =sqrt(2) cos theta prove that cos theta -sin theta =sqrt(2) sin theta

Simplify be reducing to a single term : cos 5 theta cos 2 theta - sin 5 theta sin 2 theta.