If a point P on the ellipse `x^2/a^2+y^2/b^2=1` is `(a cos theta, b sin theta)` and S, S' are the foci, then prove that `SP*S'P=a^2sin^2theta+b^2cos^2theta`.

IF the equation of the ellipse is x^2/a^2+y^2/b^2=1 then SP+S'P=

If a cos theat + b sin theta = m and a sin theta- b cos theta = n, then prove that a^2 + b^2 = m^2 + n^2

Prove the following: sin^4theta+cos^4theta=1-2sin^2thetacos^2theta

Prove that sin^4 theta - cos^4 theta = 1 - 2cos^2 theta

P and Q are two points on the ellipse x^2/a^2+y^2/b^2=1 with eccentric angles theta_1 and theta_2 . Find the equation of the locus of the point of intersection of the tangents at P and Q if theta_1+theta_2=pi/2 .

If cos theta + (1)/(cos theta) = 4 , then prove that cos^(2) theta + (1)/(cos^(2)theta) = 14.

Prove the following: cos^4theta-sin^4theta+1=2cos^2theta

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

Find (d^2 y)/(dx^2) of the following: x = a cos^3 theta , y= b sin^3 theta