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

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

If (cos^4alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 prove that (i) sin^4alpha+sin^4beta=2sin^2alphasin^2beta (ii) (cos^4beta)/(cos^2alpha)+(sin^4beta)/(sin^2alpha)=1

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

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

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

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

If tan beta = 3 tan alpha, prove that tan (alpha + beta) = (2sin 2beta)/(1+cos 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)

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

If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5-cos2beta)