sinh ^{-1} 2 + sinh ^{-1} 3 = x Rightarrow co | vedclass

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(C) Given,$\sinh ^{-1} 2 + \sinh ^{-1} 3 = x$ Taking $\cosh$ on both sides,$\cosh(\sinh ^{-1} 2 + \sinh ^{-1} 3) = \cosh x$ Using the identity $\cosh(

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given,$\sinh ^{-1} 2 + \sinh ^{-1} 3 = x$ Taking $\cosh$ on both sides,$\cosh(\sinh ^{-1} 2 + \sinh ^{-1} 3) = \cosh x$ Using the identity $\cosh(A + B) = \cosh A \cosh B + \sinh A \sinh B$,we get: $\cosh(\sinh ^{-1} 2) \cosh(\sinh ^{-1} 3) + \sinh(\sinh ^{-1} 2) \sinh(\sinh ^{-1} 3) = \cosh x$ Since $\cosh(\sinh ^{-1} y) = \sqrt{1 + y^2}$ and $\sinh(\sinh ^{-1} y) = y$: $\cosh x = \sqrt{1 + 2^2} \cdot \sqrt{1 + 3^2} + 2 \cdot 3$ $\cosh x = \sqrt{5} \cdot \sqrt{10} + 6$ $\cosh x = \sqrt{50} + 6 = \frac{2 \sqrt{50} + 12}{2} = \frac{1}{2}(12 + 2 \sqrt{50})$

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

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