The equation of locus of the point, tangents from which to `y^2=4x` are such that `cot theta_1-cot theta_2 = 5` , where `theta_1` and `theta_2` are inclination of tangents, is :

If 2tan theta-cot theta=-1 then theta= ______

Find the locus of the point P from which tangents are drawn to the parabola y^(2) = 4ax having slopes m_(1) and m_(2) such that theta_(1)-theta_(2)=theta_(0) (constant) where theta_(1) and theta_(2) are the inclinations of the tangents from positive x-axis.

The locus of the point (cot theta + cos theta, cot theta - cos theta ) where 0 le theta lt 2 pi is

If cot^4theta-cot^2 theta = 1 then show that sec^4 theta-sec^2 theta=1 .

Find the locus of the point P from which tangents are drawn to the parabola y^(2) = 4ax having slopes m_(1) and m_(2) such that m_(1)^(2)+m^(2)=lamda (constant) where theta_(1) and theta_(2) are the inclinations of the tangents from positive x-axis.

The locus of the point (cot theta+cos theta,cot theta-cos theta) where 0<=theta<2 pi is

Prove that: cot theta cot2 theta + cot2 theta cot 3 theta + 2 = cot theta(cot theta - cot3 theta)

Prove that cot theta cot 2 theta+ cot 2 theta cot 3 theta+ 2= cot theta (cot theta- cot 3 theta) .

Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot theta(cot theta - cot 3theta)