If `Delta=|(sinalpha,cosalpha,sinalpha+cosalpha),(sinbeta,cosalpha,sinbeta+cosbeta),(singamma,cosalpha,singamma+cosbeta)|` then `Delta` equals

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

Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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

Evaluate Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}|

If /_\ = |[sinalpha, cosalpha, sin(alpha+delta)],[sinbeta, cosbeta, sin(beta+delta)],[singamma, cosgamma, sin(gamma+delta)]| then prove that /_\ is independent of alpha, beta, gamma and delta.

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

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

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

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0