Question

If \[ \tanh^{-1}(x)=\log\sqrt3 \] and \[ \cosh^{-1}(y)=\log(1+\sqrt2), \] then \[ \operatorname{sech}^{-1}(xy)= \]

• A. \(\log(1+\sqrt2)\)
• B. \(\log(\sqrt3+\sqrt6)\)
• C. \(\log\sqrt2\)
• D. \(\log\sqrt3\)

Hint:

Remember the standard result: \[ \cosh^{-1}(\sqrt2)=\log(1+\sqrt2). \] It appears frequently in inverse hyperbolic function problems.

Answer 1

The Correct Option is A