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AP EAMCET · Maths · Inverse Trigonometric Functions

\(\operatorname{Tanh}^{-1}(\sin \theta)=\)

  1. A \(\operatorname{Sinh}^{-1}(\operatorname{cosec} \theta)\)
  2. B \(\operatorname{Sinh}^{-1}(\sec \theta)\)
  3. C \(\operatorname{Cosh}^{-1}(\operatorname{cosec} \theta)\)
  4. D \(\operatorname{Cosh}^{-1}(\sec \theta)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\operatorname{Cosh}^{-1}(\sec \theta)\)

Step-by-step Solution

Detailed explanation

\( y = \operatorname{Tanh}^{-1}(\sin \theta) \) \( \tanh y = \sin \theta \) \( \operatorname{sech}^2 y = 1 - \tanh^2 y = 1 - \sin^2 \theta = \cos^2 \theta \) \( \cosh y = \frac{1}{\operatorname{sech} y} = \frac{1}{\cos \theta} = \sec \theta \)…