Question

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

Answer 1

`|{:(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta)):}|=|{:(sinalpha,cosalpha,cosalphacosdelta-sinalphasindelta),(sinbeta,cosbeta,cosbetacosdelta-sinbetasindelta),(singamma,cosgamma,cosgammacosdelta-singammasindelta):}|`
`|{:(sinalpha,cosalpha,0),(sinbeta,cosbeta,0),(singamma,cosgamma,0):}|`
`(C_(3)toC_(3)+sindelta.C_(1)-cosdeltaC_(2))`
=0=R.H.S.