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TS EAMCET · Maths · Trigonometric Ratios & Identities

\(\sinh ^{-1} 2+\sinh ^{-1} 3=x \Rightarrow \cosh x\) is equal to

  1. A \(\frac{1}{2}(3 \sqrt{5}+2 \sqrt{10})\)
  2. B \(\frac{1}{2}(3 \sqrt{5}-2 \sqrt{10})\)
  3. C \(\frac{1}{2}(12+2 \sqrt{50})\)
  4. D \(\frac{1}{2}(12-2 \sqrt{50})\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{2}(12+2 \sqrt{50})\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Given, } \sinh ^{-1} 2+\sinh ^{-1} 3=x \\ & \Rightarrow \quad \cosh \left(\sinh ^{-1} 2+\sinh ^{-1} 3\right)=\cosh x \\ & \Rightarrow \quad \cosh \left(\sinh ^{-1} 2\right) \cosh \left(\sinh ^{-1} 3\right) \\ & +\sinh \left(\sinh ^{-1} 2\right) \sinh…