Prove that `cos 2a=2sin^(2)beta+4cos (alpha+beta)sin alpha sin beta+cos2(alpha+beta)`

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

Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

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

If y = sin ^(2) alpha + cos ^(2) (alpha + beta) + 2 sin alpha sin betacos(alpha+beta) then (d^(3)y)/(dalpha^(3))=?

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

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

If the sides of a right angled triangle are {cos 2 alpha + cos 2 beta + 2 cos (alpha+beta)} and {sin 2 alpha+sin 2 beta + 2 sin (alpha+beta)} then the length of the hypotneuse is

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

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)

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta