ExamBro
ExamBro
AP EAMCET · Maths · Differentiation

If \(y=\sqrt{\frac{1+\tan x}{1-\tan x}}\), then \(\frac{d y}{d x}=\)

  1. A \(\frac{1}{2}\left(\sqrt{\frac{1-\tan x}{1+\tan x}}\right) \sec ^2\left(\frac{\pi}{4}+x\right)\)
  2. B \(\frac{1}{2}\left(\sqrt{\frac{1-\tan x}{1+\tan x}}\right) \sec \left(\frac{\pi}{4}+x\right)\)
  3. C \(\left(\sqrt{\frac{1-\tan x}{1+\tan x}}\right) \sec ^2\left(\frac{\pi}{4}+x\right)\)
  4. D \(\frac{1}{2}\left(\sqrt{\frac{1+\tan x}{1-\tan x}}\right) \sec ^2\left(\frac{\pi}{4}+x\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2}\left(\sqrt{\frac{1-\tan x}{1+\tan x}}\right) \sec ^2\left(\frac{\pi}{4}+x\right)\)

Step-by-step Solution

Detailed explanation

Given, \(y=\sqrt{\frac{1+\tan x}{1-\tan x}}\)…