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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(u=\log \tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\), then \(\cosh u=\)

  1. A \(\sec \theta\)
  2. B \(\tan \theta\)
  3. C \(\operatorname{cosec} \theta\)
  4. D \(\cot \theta\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\sec \theta\)

Step-by-step Solution

Detailed explanation

\(e^u = \tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\) \(e^{-u} = \cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\) \(\cosh u = \frac{e^u+e^{-u}}{2} = \frac{\tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right) + \cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)}{2}\)…