If `(1//x)+ x =2 cos theta`, then prove that `x^(n) +1//x^(n)=2 cos n theta`

If A=[[cos theta, sin theta],[ -sin theta, cos theta]] , then prove that A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]] , n in N .

If 2costheta=x+(1/x) prove that 2cos3theta=x^3+(1/x^3)

The parametric form of the ellipse 4 (x +1) ^(2) + (y-1) ^(2) = 4 is a) x = cos theta -1 , y =2 sin theta -1 b) x = 2 cos theta-1 , y =2 sin theta -1 c) x = cos theta - 1, y = 2 sin theta + 1 d) x = cos theta +1, y =2 sin theta +1

If cos theta, sin phi, sin theta are in G.P., then prove that roots of x^(2)+2 cot phi x+1=0 are real

Prove that (sin2theta)/(1+cos2theta)=tantheta

Prove that (sin2theta)/(1-cos2theta)=cottheta

Prove that 1+cos 2x=2cos^2x .

If x=acos^3theta and y=asin^3theta . Prove that 1+(dy/dx)^2=sec^2theta .

If x = a(1+ cos theta), y = a (theta + sin theta) , then (d^(2)y)/(d x^(2)) at theta = (pi)/(2) is