If `alpha and beta` are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is `(sinalpha+sinbeta)/("sin"(alpha+beta))`

If the theta and varphi be the eccentric angles of the two ends of a focal chord of an ellipse then show that pm e "cos" (theta + varphi)/(2) = "cos" (theta- varphi)/(2)*

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

If alpha and beta be the eccentric angles of the extremities of a focal chord of the hyperbola b^(2)x^(2) - a^(2)y^(2) = a^(2)b^(2) , show that, tan(alpha)/(2)tan(beta)/(2) = -(e-1)/(e+1) , (e-1)/(e+1) (e is the eccentricity of the hyperbola.).

If (alpha+beta) and (alpha-beta) are the eccentric angles of the points P and Q respectively on the ellipse x^2/25+y^2/9=1 .Show that the equation of the chord PQ is x/5cosalpha+y/3sinalpha=cosbeta

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

If 3 sinalpha=5sin beta , then find the value of ("tan"(alpha+beta)/2)/("tan"(alpha-beta)/2)

From a point a metres above a lake the angle of elevation of a cloud is alpha and the angle of depression of its reflection is beta . Prove tha the height of the cloud is (a sin(alpha + beta))/(sin(beta-alpha)) metres.

Prove that (cos alpha - cos beta)^(2) +(sin alpha - sin beta)^(2) = 4 "sin"^(2) (alpha-beta)/2

Prove that , tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos^2alpha-sin^2beta)

Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)dot