WBJEE · Maths · Trigonometric Equations
The solution set of the equation \(\left(x \in\left(0, \frac{\pi}{2}\right)\right) \tan (\pi \tan x)=\cot (\pi \cot x)\) is
- A \(\{0\}\)
- B \(\left\{\frac{\pi}{4}\right\}\)
- C \(\phi\)
- D \(\left\{\frac{\pi}{6}\right\}\)
Answer & Solution
Correct Answer
(C) \(\phi\)
Step-by-step Solution
Detailed explanation
\(\tan (\pi \tan x)=\cot (\pi \cot x)\) or, \(\tan (\pi \tan x)=\tan \left(\frac{\pi}{2}-\pi \cot x\right)\) or, \(\quad \pi \tan x=\frac{\pi}{2}-\pi \cot x\) or, \(\tan x=\frac{1}{2}-\cot x\) or, \(\quad \tan x+\cot x=\frac{1}{2}\) or,…
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