Question

If A + B + C = $\pi$, then the value $\left|\begin{array}{ccc}\sin \left(A+B+C\right)& \sin B& \cos C\\ -\sin B& 0& \tan A\\ \cos \left(A+B\right)& -\tan A& 0\end{array}\right|$

• A. 0
• B. 1
• C. 2 sin B tan cos C
• D. none of these.

Answer 1

Answer: (A)

The given determinant is skew-symmetric of odd order (namely 3),
( $\because$ cos (A+ B) = cos ($\pi$ - C) = - cos C and sin (A + B + C) = sin $\pi$ = 0)
therefore. if $\Delta$ is the value of determinant, then $\Delta =(-1{)}^3\Delta \Rightarrow 2\Delta =0$