AP EAMCET · Maths · Inverse Trigonometric Functions
\(\operatorname{Tanh}^{-1}(\sin \theta)=\)
- A \(\operatorname{Sinh}^{-1}(\operatorname{cosec} \theta)\)
- B \(\operatorname{Sinh}^{-1}(\sec \theta)\)
- C \(\operatorname{Cosh}^{-1}(\operatorname{cosec} \theta)\)
- D \(\operatorname{Cosh}^{-1}(\sec \theta)\)
Answer & Solution
Correct Answer
(D) \(\operatorname{Cosh}^{-1}(\sec \theta)\)
Step-by-step Solution
Detailed explanation
\( y = \operatorname{Tanh}^{-1}(\sin \theta) \) \( \tanh y = \sin \theta \) \( \operatorname{sech}^2 y = 1 - \tanh^2 y = 1 - \sin^2 \theta = \cos^2 \theta \) \( \cosh y = \frac{1}{\operatorname{sech} y} = \frac{1}{\cos \theta} = \sec \theta \)…
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