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

"cosec" theta =1/2

Show that cot theta +tan theta =sec theta cosec theta

If "cosec" theta + cot theta = (13)/5 then cot^(2) theta - "cosec"^(2) theta = (25)/12

If : cot theta + cot((pi)/4 + theta) = 2 , then : 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 costheta + sin theta = sqrt2 cos theta , prove that cos theta - sin theta = sqrt2 sin theta .

If cos(theta+phi)=mcos(theta-phi) , then prove that tantheta=(1-m)/(1+m)cotphi .

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

If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)theta = 1