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AP EAMCET · Maths · Basic of Mathematics

If \(x=\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right]\), then the value of \(\sin h x\) is

  1. A \(\tan 2 \theta\)
  2. B \(\ -tan 2 \theta\)
  3. C \(\cot 2 \theta\)
  4. D \(\ -cot 2 \theta\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\ -tan 2 \theta\)

Step-by-step Solution

Detailed explanation

Give that, \(x=\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right]\) \(e^x=\left[\cot \left(\frac{\pi}{4}+\theta\right)\right]...(i)\) and \(e^{-x}=\frac{1}{\cot \left(\frac{\pi}{4}+\theta\right)}=\tan \left(\frac{\pi}{4}+\theta\right)...(ii)\) We know that,…