Quantitative Aptitude Ques 822

Question: The value of $ \cot \frac{\pi }{2}\cot \frac{3\pi }{20}\cot \frac{5\pi }{20}\cot \frac{7\pi }{20}\cot \frac{9\pi }{20} $

Options:

A) $ -1 $

B) $ \frac{1}{2} $

C) $ 0 $

D) $ 1 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ \cot \frac{\pi }{20}\cdot \cot \frac{3\pi }{20}\cdot \cot \frac{5\pi }{20}\cdot \cot \frac{7\pi }{20}\cot \frac{9\pi }{20}\cdot $ $ =\cot ( \frac{\pi }{2}-\frac{9\pi }{20} )\cot ( \frac{\pi }{2}-\frac{7\pi }{20} )\cot ( \frac{\pi }{4} )\cot \frac{7\pi }{20}\cot \frac{9\pi }{20} $ $ =\tan ( \frac{9\pi }{20} )\tan ( \frac{7\pi }{20} )\cot ( \frac{\pi }{4} )\cot ( \frac{7\pi }{20} )\cot ( \frac{9\pi }{20} ) $ $ =1.1.1=1 $ $ [ \because \cot \frac{\pi }{4}=1,and,cot\theta \cdot tan\theta =1 ] $
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