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

Prove that cos(alpha+beta )=cosalphacosbeta-sinalphasinbeta

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

If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1 , where alpha and beta do not differ by an even multiple of pi , prove that (cos alpha cos beta)/(cos^(2)A)+(sin alpha sin beta)/(sin^(2)A)=

If (sin alpha)/(sin beta)=(cos gamma)/(cos delta), then (sin ((alpha-beta)/2) . cos ((alpha+beta)/2) . cos delta)/(sin ((delta-gamma)/2) . sin ((delta+gamma)/2) . sin beta)

If x =cos alpha+cos beta-cos(alpha+beta) and y=4 sin.(alpha)/(2)sin.(beta)/(2)cos.((alpha+beta)/(2)) , then (x-y) equals

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)

If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)

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