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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Determinants

NDA 2021 · Mathematics · Determinants

What is the value of the following determinant? | array ccc C & A &...

What is the value of the following determinant? \left|cos⁡Ctan⁡A0sin⁡B0−tan⁡A0sin⁡Bcos⁡C\begin{array}{ccc} \cos C & \tan A & 0 \\ \sin B & 0 & -\tan A \\ 0 & \sin B & \cos C \end{array}\right|

Options

  1. A-1
  2. B0
  3. C2tan⁡Asin⁡Bsin⁡C2 \tan A \sin B \sin C
  4. D−2tan⁡Asin⁡Bsin⁡C-2 \tan A \sin B \sin C

Correct answer

B. 0

Step-by-step solution

cos⁡C(tan⁡A⋅sin⁡B)−tan⁡A(sin⁡B⋅cos⁡C)=0\cos C(\tan A \cdot \sin B)-\tan A(\sin B \cdot \cos C)=0
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