If `x=ptantheta+ qsectheta` and `y=psectheta+qtantheta` the prove that `x^2-y^2=q^2-p^2`.

x = a sec theta + b tan theta and y= a tan theta + b sec theta. Prove that x^(2)-y^(2) = a^(2)-b^(2) .

If x=r cos theta, y=r sin theta Prove that x^(2)+y^(2)=r^(2)

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

If x = acos^(3)theta sin^(2)theta , y = asin^(3)theta cos^(2)theta and (x^(2) + y^(2))^(p)/(xy)^(q)(p,q in N) is independent of theta , then :

The straight line x+y=-sqrt2P will touch the hyperbola 4x^2-9y^2=36 if

If x+iy = (a+ib)/(a-ib) , prove that x^(2) + y^(2)=1 .

If x+iy=(a+ib)/(a-ib) , prove that x^(2)+y^(2)=1

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

If y= A sin x+ B cos x , then prove that (d^(2)y)/(dx^(2))+y=0 .

If x+iy=(2+i)/(2-i) then prove taht x^(2)+y^(2)=1