`[{:(sinalpha,cosalpha,sin(alpha+delta)),(sinbeta,cosbeta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta)):}]=`

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 ) |:} =1

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

The determinant : |(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sinalpha,cosalpha,sinbeta),(-cosalpha,sinalpha,cosbeta)|=0 is independent of :

If A=|(1+cosalpha,1+sinalpha,1),(1+cosbeta,1+sinbeta,1),(1,1,1)|ne0 , then :

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

The real part of [[cos alpha+i sin alpha, cos beta+i sin beta],[ sin beta+i cos beta, sin alpha+i cos alpha]] is

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

If alpha, beta and gamma are angles such that tan alpha+tan beta+tan gamma=tan alpha . tan beta . tan gamma and x=cos alpha+i sin alpha, y=cos beta+i sin beta and z=cos gamma+i sin gamma , then x y z=

sin(3theta+alpha)+sin(3theta-alpha)+sin(alpha-theta)-sin(alpha+theta)=cosalpha