The value of | * 20 c & & ( + ) & & ( + ) & & ( + ) | is - Vidyadip

MCQ

The value of $\left| {\begin{array}{*{20}{c}}
{\sin \alpha }&{\cos \alpha }&{\sin \left( {\alpha + \gamma } \right)}\\
{\sin \beta }&{\cos \beta }&{\sin \left( {\beta + \gamma } \right)}\\
{\sin \delta }&{\cos \delta }&{\sin \left( {\gamma + \delta } \right)}
\end{array}} \right|$ is

A
$\sin \alpha \sin \beta \sin \delta $
B
$\cos \alpha \cos \beta \cos \delta $
C
$1$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
Apply $\mathrm{C}_{3} \rightarrow \mathrm{C}_{3}-\cos \gamma . \mathrm{C}_{1}$

$\Delta = \left| {\begin{array}{*{20}{c}}
{\sin \alpha }&{\cos \alpha }&{\cos \alpha \sin \gamma }\\
{\sin \beta }&{\cos \beta }&{\cos \beta \sin \gamma }\\
{\sin \delta }&{\cos \delta }&{\cos \delta \cos \gamma }
\end{array}} \right|$

$\Delta=0$

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