If a chord joining the points `P (a sec theta, a tan theta) & Q (a sec phi, a tan phi)` on the hyperbola `x^2 - y^2 = a^2` is a normal to it at P, then show that `tan phi = tan theta (4 sec^2 theta – 1)`.

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha =

If a chord joining P(a sec theta, a tan theta), Q(a sec alpha, a tan alpha) on the hyperbola x^(2)-y^(2) =a^(2) is the normal at P, then tan alpha is (a) tan theta (4 sec^(2) theta+1) (b) tan theta (4 sec^(2) theta -1) (c) tan theta (2 sec^(2) theta -1) (d) tan theta (1-2 sec^(2) theta)

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^@ - y^2/b^2 = 1 passes through a focus, prove that tan theta/2 tan phi/2 + (e-1)/(e+1) = 0 .

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^2 - y^2/b^2 = 1 passes through a focus, prove that tan (theta/2) tan (phi/2) + (e-1)/(e+1) = 0 .

Show that tan (pi/4+theta/2)=sec theta +tan theta .

If sec theta+tan theta=2 , then sec theta-tan theta = ?

If tan theta = p - (1)/(4p) then sec theta - tan theta =