If `cos^-1 frac {x}{2} + cos^-1 frac {y}{3}= theta`, prove that : `9x^2-12 xy cos theta + 4 y^2= 36 sin^2theta`.

If cos^-1 frac {x}{a} + cos^-1 frac {y}{b}= alpha , prove that : frac {x^2}{a^2}- frac{2xy}{ab} cos alpha + frac {y^2}{b^2}= sin^2 alpha

If cos theta =1/2(a+1/a) , prove that : 2 cos 4 theta= a^4+1/ a^4 .

Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta .

Find dy/dx , if x = cos(theta) and y = sin(2theta)

Prove that : sin 2 theta= 2sin theta cos theta .

Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

Show that the equations of the normal at any point theta on the curve x = 3 cos theta - cos^3 theta, y = 3 sin theta - sin ^3 theta is 4(y cos^3 theta - x sin^3 theta) = 3 sin 4 theta

If x cos theta- y sin theta=a,x sin theta+ y cos theta=b , prove that x^2+y^2= a^2+b^2 .

Prove that : sin^-1 frac{3}{5} + sin^-1 frac{8}{17}= cos^-1 frac{36}{85}