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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sinh x=\frac{5}{12}\), then \(\cosh \frac{x}{2}=\)

  1. A \(\frac{3}{2 \sqrt{5}}\)
  2. B \(\frac{2}{3 \sqrt{3}}\)
  3. C \(\frac{5}{\sqrt{6}}\)
  4. D \(\frac{5}{2 \sqrt{6}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{5}{2 \sqrt{6}}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \sinh x=\frac{5}{12} \\ & \because \cosh x=2 \cosh \frac{x}{2}-1=\sqrt{1+\sin h^2 \frac{x}{2}} \\ & \Rightarrow 2 \cosh ^2 \frac{x}{2}-1=\sqrt{1+\left(\frac{5}{12}\right)^2} \\ & \Rightarrow 2 \cosh ^2 \frac{x}{2}=\frac{13}{12}+1=\frac{25}{12}…