The value of the determinant `Delta = |(sin 2 alpha,sin (alpha + beta),sin (alpha + gamma)),(sin (beta + gamma),sin 2 beta,sin (gamma + beta)),((sin gamma + alpha),sin (gamma + beta),sin 2 gamma)|`, is
A. 0
B. `sin^(2) alpha + sin^(2) beta + sin^(2) gamma`
C. `(3)/(2)`
D. None of these

Options

A. 0
B. `sin^(2) alpha + sin^(2) beta + sin^(2) gamma`
C. `(3)/(2)`
D. none of these

Answer

A

Explanation

We have,
`Delta = |(sin alpha,cos alpha,0),(sin beta,cos beta,0),(sin gamma,cos gamma,0)| |(cos alpha,sin alpha,0),(cos beta,sin beta,0),(cos gamma,sin gamma,0)|`
`rArr Delta= 0 xx 0 = 0`