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 (a sec theta, b tan theta) and (a sec phi, b tan phi) are the ends of a focal chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then prove that tan.(theta)/(2)tan.(phi)/(2)=(1-e)/(1+e) .

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(theta/2)tan(phi/2)=(1-e)/(1+e)

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)

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)

If (a sec theta;b tan theta) and (a sec phi;b tan phi) 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)

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

IF alpha , beta are eccentric angles of end points of a focal chord of the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 then tan(alpha /2) tan (beta/2) is equal to

If theta_(1) and theta_(2) are the parameters of the extremities of a chord through (ae,0) of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 then tan((theta_(1))/(2))tan((theta_(2))/(2))=

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 .