If `sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(2)`, then `(sin alpha+cos beta)` is equal to

Ifsin^(4)alpha+cos^(4)beta+2=4sin alpha cos beta,0<=alpha,beta<=(pi)/(2) then find the value of (sin alpha+cos beta)

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

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

If cos alpha+cos beta=0=sin alpha+sin beta, then cos2 alpha+cos2 beta is equal to

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

sin^(4)alpha+4cos^(4)beta+2=4sqrt(2)sin alpha cos beta;alpha,beta in[0,pi], then cos(alpha+beta)-cos(alpha-beta) is equal to :

csc^(2)(alpha+beta)-sin^(2)(beta-alpha)+sin^(2)(2 alpha-beta)=cos^(2)(alpha-beta) where alpha,beta in(0,(pi)/(2)), then sin(alpha-beta) is equals