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If p and q are the lengths of perpendicu...

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`.

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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) .

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

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

Prove the following identity : sin theta (1+tan theta)+ cos theta(1+cot theta)= sec theta+ cosec theta .

if x = sec theta - cos theta and y = sec^n theta - cos^n theta , then show that (x^2+4)(dy/dx)^2 = n^2(y^2+4)

If x = 2 cos theta - cos 2 theta, y = 2 sin theta - sin 2 theta, find dy/dx at theta = pi/2

Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= tan theta+ cot theta= sec theta cosec 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 .

PSEB-STRAIGHT LINES-EXERCISE
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