Number of points on the staight line `x+y+2 sqrt2=0`, which are at a distance of `sin^3 theta+cos^3 theta, theta in [0,pi]`

The number of points on the straight line x+y+2sqrt(2)=0, which are at a distance of sin^(3)theta+cos^(3)theta,theta in[0,(pi)/(2)] from origin is (B) 0 (B) 1 (C) 2 (D) infinite

The number of distinct solutions of sin5 theta*cos3 theta*cos7 theta=0 in [0,(pi)/(2)] is :

The number of solutions of the pair of equations 2sin^2 theta - cos(2 theta)=0,2cos^2 theta-3sin theta=0 in the interval [0,2pi] is

If (alpha,beta) is a point of intersection of the lines x cos theta+y sin theta=3 and x sin theta-y cos theta=4 where theta is parameter,then maximum value of 2(a+beta)/(sqrt(2)) is

Solve 3 cos^2 theta - 2 sqrt3 sin theta cos theta - 3 sin^2 theta = 0

If beta is one of the angles between the normals to the ellipse, x^2+3y^2=9 at the points (3 cos theta, sqrt(3) sin theta)" and "(-3 sin theta, sqrt(3) cos theta), theta in (0,(pi)/(2)) , then (2 cos beta)/(sin 2 theta) is equal to:

If beta is one of the angles between the normals to the ellipse, x^2+3y^2=9 at the points (3 cos theta, sqrt(3) sin theta)" and "(-3 sin theta, sqrt(3) cos theta), theta in (0,(pi)/(2)) , then (2 cot beta)/(sin 2 theta) is equal to:

If 0