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

If m= sin theta+ cos theta and n= sec theta+cosec theta , prove that n (m + 1) (m-1) = 2m .

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

Prove the following identity : sin theta cot theta+ sin theta cosec theta=1 + cos theta .

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec theta .

Prove the following identity : (tan theta-cot theta)/ (sin theta cos theta)= sec^2 theta- cosec^2 theta .

If p and q are respectively the perpendiculars from the origin upon the striaght 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

Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 theta)

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Find dy/dx when x = a (cos theta + theta sin theta) , y = a (sin theta - theta cos theta).