`{:|( sin alpha , cos alpha ,cos (alpha +delta) ),( sinbeta, cos beta,cos (beta+delta )),(sin gamma , cos gamma , cos ( gamma +delta ))|:}=0`

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

prove that, |{:(sin^2alpha,sin alpha cosalpha,cos^2alpha),(sin^2beta,sinbetacosbeta,cos^2beta),(sin^2gamma,singammacosgamma,cos^2gamma):}|=-sin(alpha-beta)sin(beta-gamma)sin(gamma-alpha)

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 ) |:} =0

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

|{:(cosalpha cos beta,cos alpha sin beta ,-sin alpha),(-sin beta,cos beta," "0),(sin alpha cosbeta ,sinalpha sin beta ,""cos alpha):}|

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

"Evaluate "Delta ={:|( 0 , sin alpha ,-cos alpha ) ,( -sin alpha , 0 , sin beta ),( cos alpha , -sin beta , 0)|:}

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4

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

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (sin alpha - cos alpha - sin beta + cos beta)/(sin alpha + cos alpha - sin beta - cos beta)=