Find perpendicular distance from the origin of the line joining the points `(cos theta, sin theta)` and `(cos phi, sin phi)`

Find the slope of the line joining the points (a cos theta , b sin theta) and (a cos phi, b sin phi)

If p and q are the lenghts of the perpendiculars from the origin to the lines x cos theta - y sin theta = k cos 2theta and x sec theta + y cosec theta = k respectively prove that p^2 + 4q^2= k^2

If the line joining the points (a cos theta , b sin theta) and (a cos phi, b sin phi) .Prove that the equation of this lines is x/a "cos" (theta + phi)/2 + y/b"sin" (theta + phi)/2 = "cos" (theta -phi)/2

The number of solutions of cos 2 theta = sin theta in (0, 2pi) is

If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are x sec theta + y cosec theta = a and x cos theta - y sin theta =a cos 2 theta, then 4p ^(2) + q ^(2) is equal to a) 5a^(2) b) 4a ^(2) c) 3a ^(2) d) 2a ^(2)

Prove that sin (3theta)/(1+2cos 2theta)=sin theta .

If p_(1)andp_(2) are respectively length of perpendiculars from the origin to the straight lines x"sec"theta+y"cosec"theta=a " " and x "cos"theta-y"sin"theta=a"cos"2theta , then 4p_(1)^(2)+p_(2)^(2) is equal to

Express each one of the following in the standard form a+ib (1)/(1-cos theta+2i sin theta)

Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|