Relation between 'alpha'and 'beta'is `alpha=beta/(1+beta)`.Define `alpha and `beta`.

Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -sin beta, cos beta, 0],[ sin alpha cos beta, sin alpha sin beta, cos alpha]|

If A(alpha, beta) = [(cos alpha, sin alpha, 0),(- sin alpha, cos alpha, 0),(0,0,e^beta)] then A(alpha, beta)^(-1) is equal to a) A(-alpha, -beta) b) A(-alpha,beta) c) A(alpha, - beta) d) A(alpha, beta)

|(alpha,-beta,0),(0,alpha,beta),(beta,0,alpha)|=0 , then

If cosalpha+cosbeta=0=sinalpha+sinbeta,cos2alpha+cos2beta is equal to a) -2sin(alpha+beta) b) 2cos(alpha+beta) c) 2sin(alpha-beta) d) -2cos(alpha+beta)