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`.

If the chord through the points whose eccentric angles are theta and varphi on the ellipse (x^2)/(25)+(y^2)/9=1 passes through a focus, then the value of tan(theta/2)tan(varphi/2) is 1/9 (b) -9 (c) -1/9 (d) 9

If the chords through point theta and phi on the ellipse x^2/a^2 + y^2/b^2 = 1 . Intersect the major axes at (c,0).Then prove that tan theta/2 tan phi/2 = (c-a)/(c+a) .

If (asectheta;btantheta) and (asecphi; btanphi) are the ends of the focal chord of x^2/a^2-y^2/b^2=1 then prove that tan(x/a)tan(phi/2)=(1-e)/(1+e)

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

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 (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of the ends of a focal chord passing through (ae,0) of x^2/a^2-y^2/b^2=1 then tan(theta/2)tan(phi/2) equals to

If 1+ tan^(2) theta = sec^(2) theta then find (sec theta + tan theta)

Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta .

Prove that 1 + tan 2 theta tan theta = sec 2 theta .

Prove that (tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta