Without expanding evaluate the determinant `|sinalphacosalphasin(alpha+delta)sinbetacosbetasin(beta+delta)singammacosgammasin(gamma+delta)|` .

Answer

`D=0`

Explanation

Let the given determinant be `\Delta`.
Then, applying `C_{3} \rightarrow C_{3}+(\sin \delta) C_{1}-(\cos \delta) C_{2}`
$$\Delta=\left|\begin{array}{ccc}\sin \alpha & \cos \alpha & 0 \\ \sin \beta & \cos \beta & 0 \\ \sin g \gamma & \cos \gamma & 0\end{array}\right|=0\left[\because\right. \text{ each element in}\left.C_{3} \text{ is } 0 \right]$$