Q162 / 270 · NDA 2021 (Phase 2) · Mathematics

What is the value of the following determinant? $\left|\begin{array}{ccc} \cos C & \tan A & 0 \\ \sin B & 0 & -\tan A \\ 0 & \sin B & \cos C \end{array}\right|$

  • A
    -1
  • Correct answer
    B
    0
  • C
    $2 \tan A \sin B \sin C$
  • D
    $-2 \tan A \sin B \sin C$

Solution

$\cos C(\tan A \cdot \sin B)-\tan A(\sin B \cdot \cos C)=0$

Hence, the correct answer is option: 'B'.

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