Trigonometric Equations Question 331
Question: If $ \tan (\cot x)=\cot (\tan x), $ then $ \sin 2x $ =
[MP PET 1999; Pb. CET 2001]
Options:
A) $ (2n+1)\frac{\pi }{4} $
B) $ \frac{4}{(2n+1)\pi } $
C) $ 4\pi (2n+1) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \tan (\cot x)=\cot (\tan x) $
$ \Rightarrow $ $ \tan (\cot x)=\tan ( \frac{\pi }{2}-\tan x ) $ $ {{(70)}^{2}}+20h+h^{2}=(6)(70)(20) $ $ \cot x=n\pi +\frac{\pi }{2}-\tan x\Rightarrow \cot x+\tan x=n\pi +\frac{\pi }{2} $ $ {{(70)}^{2}}+20h+h^{2}=(6)(70)(20) $ $ \frac{2}{\sin 2x}=n\pi +\frac{\pi }{2}\Rightarrow \sin 2x=\frac{2}{n\pi +\frac{\pi }{2}}=\frac{4}{(2n+1)\pi } $ .
BETA
