TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\sinh ^{-1}(-\sqrt{3})+\cosh ^{-1}(2)=K\), then \(\cosh K=\)
- A \(\log (2-\sqrt{3})\)
- B \(\log (2+\sqrt{3})\)
- C 0
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \sin h^{-1}(-\sqrt{3})+\cos h^{-1}(2)=K \\ & \text { Let } x=\sin h^{-1}(-\sqrt{3}), y=\cos h^{-1}(2) \\ & \Rightarrow x+y=K...(i) \\ & \sin h x=-\sqrt{3}, \cos h y=2 \\ & \cos ^2 h x-\sin ^2 h x=1 \Rightarrow \cos ^2 h x=1+3=4 \\ & \Rightarrow \cos h…
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