Prove that `sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta)` is independent of `alpha`.

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

Prove that sin^(2)alpha+cos^(2)(alpha+beta)+2sinalphasinbetacos(alpha+beta) is independent of alpha .

Statement-I : If f(theta)=(cot theta)/(1+cot theta) and alpha+ beta=(5pi)/(4) then f(alpha) f(beta)=(1)/(2) Statement-II : If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then tan alpha= tan beta+ 2tan gamm Statement-III sin^(2) alpha+ cos^(2) (alpha+ beta)+2 sin alpha beta cos (alpha+beta) is independent of alpha only

sin alpha=sinbeta, cos alpha=cos beta then

If sin alpha = sin beta and cos alpha = cos beta then

If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

Prove that cos^(2)(alpha-beta)+cos^(2)beta-2cos(alpha-beta)cosalphacosbeta is independent of beta .

If cos alpha+cos beta=0=sin alpha+sin beta , then cos 2 alpha+cos 2beta is equal to

If sin alpha + sin beta = a , cos alpha + cos beta = b " then cos ( alpha + beta ) =