If `cos beta` is the geometric mean of `sin alpha and cos alpha,` then show that `cos 2 beta= -2 cos^(2) ((pi)/(4)+alpha)`

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

If tan^2 alpha = 1 + 2 tan^2 beta , show that cos2 beta = 1 + 2cos 2alpha .

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

If sin 2 alpha + sin 2 beta = 3 "and" cos 2 alpha + cos 2 beta = 4,"then"- cos2 (alpha + beta)=

If sin 2 alpha + sin 2 beta = 3 "and" cos 2 alpha + cos 2 beta = 4,"then"- sin 2 ( alpha + beta)

If cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If cotalphacotbeta=3 ,show that (cos(alpha-beta))/(cos(alpha+beta))=2

If alpha and beta are complementary angles, then show that cot beta+cos beta= (cos beta)/(cos alpha) (1+sin beta) .

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =