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AP EAMCET · Maths · Inverse Trigonometric Functions

If \(\cos \alpha=\operatorname{sech} \beta\), then \(\beta=\)

  1. A \(\log (\sec \alpha+\tan \alpha)\)
  2. B \(\log (\sec \alpha-\tan \alpha)\)
  3. C \(\log (\sin \alpha+\cos \alpha)\)
  4. D \(\log (\cos \alpha+\cot \alpha)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\log (\sec \alpha+\tan \alpha)\)

Step-by-step Solution

Detailed explanation

\(\cos \alpha = \operatorname{sech} \beta\) \(\beta = \operatorname{arcsech}(\cos \alpha)\) \(\beta = \log\left(\frac{1 + \sqrt{1 - \cos^2 \alpha}}{\cos \alpha}\right)\) \(\beta = \log\left(\frac{1 + \sqrt{\sin^2 \alpha}}{\cos \alpha}\right)\)…