(f) Prove that `(x sin theta - ycos theta)^2 + ( xcos theta + y sin theta)^2 = x^2 +y^2`

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

Prove that (2 sin theta - sin 2theta)/(2 sin theta + sin 2theta) = tan^2\ theta/2

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

Prove that cos^2 theta cosec theta+sin theta=cosec theta

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

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

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that : x cos theta + y sin theta = a and x sin theta - y cos theta = b are the parametric equations of a circle for all theta satisfying 0le thetalt2pi

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

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