If `alpha and beta` are non-zero real number such that `2(cos beta-cos alpha)+cos alpha cos beta=1.` Then which of the following is treu?

Let alpha and beta be non-zero real numbers such that 2 ( cos beta - cos alpha) + cos alpha cos beta =1 . Then which of the following is/are true ?

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

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=

cos (alpha-beta) quad cos (alpha-beta), cos alpha1, cos betacos alpha, cos beta, 1] |

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

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

If alpha,beta,gamma are three real numbers and A=[1"cos"(alpha-beta)"cos"(alpha-gamma)cos(beta-alpha)1"cos"(beta-gamma)"cos"(gamma-alpha)"cos"(gamma-beta)1] , then which of following is/are true? A is singular b. A is symmetric c. A is orthogonal d. A is not invertible

(cos alpha + cos beta)/( sin alpha - sin beta) + (sin alpha + sin beta)/( cos alpha - cos beta ) =