Prove that the equation of the chord joining the points 'a'&'b' on the ellipse `x^2/a^2+y^2/b^2=1` is `x/a cos((alpha+beta)/2)+y/b sin((alpha+beta)/2)=cos((alpha-beta)/2)`

Find the equation of the chord joining point P(alpha) and Q(beta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.

IF alpha,beta are the eccentric angles of the extremities of a focal chord of the ellipse x^2/a^2+y^2/b^2=1 . Then show that e cos""(alpha+beta)/2=cos""(alpha-beta)/2

P( asec alpha, b tan alpha ) and Q (a sec beta, b tan beta) are two given points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1. Show that the equation of the chord PQ is (x)/(a) cos (alpha - beta)/(2) - (y)/(b) sin (alpha + beta)/(2) = cos (alpha+beta)/(2).

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

s(theta-alpha)=a and cos(theta-beta)=b, then sin^(2)(alpha-beta)+2ab cos(alpha-beta)=

For alpha , beta in R , prove that (cos alpha + cos beta )^(2)+ (sin alpha + sin beta )^(2)=4cos^(2). ((alpha-beta))/(2)

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

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