If `cosec theta + cot theta =k ,` then prove that `cos theta =(k^(2)-1)/( k^(2)+1)`

If sec theta + tan theta = k, cos theta =

If cosec theta = 61/60, sec theta = 61/11 then cot theta =

If "cosec" theta - sin theta = a^(3) and sec theta - cos theta = b^(3) , then prove that a^(2)b^(2)(a^(2) + b^(2))= 1.

Solve cot theta + tan theta=2 cosec theta .

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

If theta + phi = alpha and tan theta = k tan phi , then prove that sin (theta - phi) = (k - 1)/(k + 1) sin alpha .

If x= a (theta+ sin theta), y =a ( 1- cos theta) then prove that at theta = (pi)/(2), y'' = (1)/(a) .

If theta + phi =alpha and tan theta = k tan phi , then prove that sin(theta - phi) =(k-1)/(k+1) sin alpha .

Prove that: cos^2 theta (1 + tan^2 theta) = 1

If cosec theta =(25)/( 7), then find cot theta