AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(u=\log \tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\), then \(\cosh u=\)
- A \(\sec \theta\)
- B \(\tan \theta\)
- C \(\operatorname{cosec} \theta\)
- D \(\cot \theta\)
Answer & Solution
Correct Answer
(A) \(\sec \theta\)
Step-by-step Solution
Detailed explanation
\(e^u = \tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\) \(e^{-u} = \cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\) \(\cosh u = \frac{e^u+e^{-u}}{2} = \frac{\tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right) + \cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)}{2}\)…
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