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GUJCET · Maths · Determinants
\(\left|\begin{array}{cc}\sin \frac{11 \pi}{36} & \cos \frac{11 \pi}{36} \\\sin \frac{2 \pi}{9} & \cos \frac{2 \pi}{9}\end{array}\right|=\) _________ .
- A \(\sin \frac{7 \pi}{12}\)
- B \(\cos \frac{\pi}{12}\)
- C \(\cos \frac{5 \pi}{12}\)
- D \(\sin \frac{2 \pi}{9}\)
Answer & Solution
Correct Answer
(C) \(\cos \frac{5 \pi}{12}\)
Step-by-step Solution
Detailed explanation
\( = \sin \frac{11 \pi}{36} \cos \frac{2 \pi}{9} - \cos \frac{11 \pi}{36} \sin \frac{2 \pi}{9} \) \( = \sin\left(\frac{11 \pi}{36} - \frac{2 \pi}{9}\right) \)
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