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

cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta=

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

The expression cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta , is

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

|(cos (alpha+beta),-sin (alpha+beta),cos 2 beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)| is independent of

Prove that |cos alpha - cos beta| le | alpha - beta| .

[(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(sin alpha-sin beta)]^n=

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

(i) sin (alpha + beta) = sin alpha cos beta + cos alpha sin beta) (ii) sin (alpha-beta)= sin alpha cos beta- cos alpha sin beta Proof