If `(cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1`,then prove that
`sin^4alpha+sin^4beta=2sin^2alphasin^2beta`.

If (cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 ,then prove that (cos^4beta)/(cos^2alpha)+(sin^4beta)/(sin^2alpha)=1

If cos^(2)alpha-sin^(2)alpha=tan^(2)beta , then prove thta tan^(2)alpha=cos^(2)beta-sin^(2)beta .

If cos alpha+cos beta=1/3 and sin alpha+sin beta=1/4 ,show that tan((alpha+beta)/2)=3/4

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 line makes alpha,beta,gamma with x,y,z axis respectively, then prove that sin^2alpha+sin^2beta+sin^2gamma=2

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)

If A_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

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