Prove that the product of the lengths of the per-pendiculars drawn from the points `(sqrt(a^2-b^2),0)` and `(-sqrt(a^2-b^2),0)` to the line `x/a cos theta+y/b sin theta=1` is `b^2` .

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2), 0) and (-sqrt(a^2-b^2), 0) to the line x/a cos theta+y/b sin theta=1 is b^2 .

Prove that : sin 2 theta= 2sin theta cos theta .

If cos 2 theta =(sqrt(2)+1)( cos theta -(1)/(sqrt(2))) , then the value of theta is

Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4) .

If sin theta=sqrt3/2 and cos theta= -1/2 then theta lies in :

If p is the length of the perpendicular from the origin to the line (x)/(a) + (y)/(b) = 1, "then prove that " (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2))

If tan theta =a/b , prove that a sin 2 theta+b cos 2 theta=b .

If y = 2/(sqrt(a^2 - b^2)) "tan"^(-1) (sqrt((a + b)/(a - b)) " tan " x/2) , prove that (dy)/(dx) = 1/(a - b cos x)

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) .

Let sin theta= -1/2 and cos theta= -sqrt3/2 , then theta lies in :