बिना प्रसार किये सिद्ध कीजिए कि
`|{:(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta)):}|=0`

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

|(sin alpha, cosalpha,sin(alpha+delta)),(sinbeta, cos beta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|=

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

sin alpha, cos alpha, cos (alpha + delta) sin beta, cos beta, cos (beta + delta) sin gamma, cos gamma, cos (gamma + delta)] | = 0

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

Using properties of determinants in Exercise 11 to 15 prove that |{:(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta)):}|=0

Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[sinalpha,cosgamma,cos(gamma+delta)]] =0