If `x=sectheta - tantheta` and `y = cosec theta+ cottheta`, then prove that `xy +1 = y - x.`

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If cos theta + sin theta = p and sec theta + cosec theta = q , prove that q (p^(2) - 1) = 2p .

If x sin^(3)theta + y cos^(3)theta = sintheta costheta and x sin theta = y cos theta , prove that x^(2) + y^(2) = 1.

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 cottheta+tantheta=2cosectheta, then find the general value of theta .

Prove that sqrt ((1+cos theta )/( 1-cos theta ) ) = cosec theta +cot theta , 0le theta le 90 ^(@)

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

P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.

If tantheta+sectheta=1. 5 , find sintheta,tanthetaa n dsecthetadot

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)