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

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

The number of ordered pairs (alpha,beta) , where alpha,betain(-pi,pi) satisfying cos(alpha-beta)=1 andcos(alpha-beta)=1 and cos(alpha+beta)=1/e is

If cos alpha = k cos beta Show that tan ((alpha+beta)/2)=(1-k)/(1+k)cot((alpha-beta)/2)

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

If alpha ne beta " and " a tan alpha + b tan beta = (a + b) "tan" (alpha + beta)/2,"show that" (cos alpha)/(cos beta) = a/b.

For all values of alpha,beta,gamma prove that: cos alpha + cos beta+ cos gamma+ cos(alpha+beta+gamma) ="4cos"(alpha+beta)/2cdot"cos" (beta+gamma)/2cdot"cos"(gamma+alpha)/2

If " "cos(alpha - beta) + 1 = 0," show that ", cosalpha + cos beta = 0 " and " sin alpha + sin beta = 0.

sin alpha + sin beta = a "and" cos alpha + cos beta = b (tan alpha + tan beta)/(1-tan alpha tan beta)=

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

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.