The coordinates of a moving point P are `(a/2(cosectheta+sintheta), b/2(cosectheta-sintheta)), " where " theta` is a variable parameter. Show that the equation of the locus P is `b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2)`.

The coordinates of a moving point P are ((a)/(2)(co sectheta+sin theta),(b)/(2)(co sec theta-sin theta)) where theta is a variable parameter. Show that the equation of the locus of P is b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2)

(sintheta+sin2theta)/(1+costheta+cos2theta)

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

Prove that (sintheta+cosectheta)^2+(costheta+sectheta)^2ge9 .

Solve the equation 2cos^2theta+3sintheta=0

If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is (x)/(a)+(y)/(b)=2

If x=a sec theta and y=b tan theta then b^(2)x^(2)-a^(2)y^(2) =_____.

If costheta +sintheta =sqrt2costheta , show that costheta -sintheta =sqrt2sintheta .

If sintheta=costheta then 2tan^(2)theta+sin^(2)theta-1=___ .