The value of $\begin{vmatrix}\sin α &\cos α &\sin (α + δ)\\\sin β &\cos β &\sin (β + δ)\\\sin γ &\cos γ &\sin (γ + δ)\end{vmatrix}$, is
Answer & explanation
Correct answer: option 1
We have,
$Δ=\begin{vmatrix}\sin α &\cos α &\sin α\, \cos δ+\cos α\,\sin δ\\\sin β &\cos β &\sin β\, \cos δ+\cos β\,\sin δ\\\sin γ &\cos γ &\sin γ\, \cos δ+\cos γ\,\sin δ\end{vmatrix}$
$⇒Δ=\begin{vmatrix}\sin α &\cos α &0\\\sin β &\cos β &0\\\sin γ &\cos γ &0\end{vmatrix}$ Applying $[C_3→C_3-\cos δ\, C_1, C_3→C_3-\sin δ\, C_2]$
$⇒Δ=0$ [∵ $C_3$ consists of all zeros]