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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sin \mathrm{h} x=\frac{\sqrt{21}}{2}\) then \(\cosh 2 x+\sinh 2 x=\)

  1. A \(\frac{21}{2}\)
  2. B \(\frac{25}{2}\)
  3. C \(\frac{23+5 \sqrt{21}}{2}\)
  4. D \(\frac{32+5 \sqrt{23}}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{23+5 \sqrt{21}}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \quad \sinh x=\frac{\sqrt{21}}{2}, \cosh x=\sqrt{1+\sin ^2 h x}=\frac{\sqrt{25}}{2}=\frac{5}{2} \\ & \sinh 2 x=2 \sinh x \cosh x=\frac{5 \sqrt{21}}{2} \\ & \cosh 2 x=\cosh ^2 x+\sinh ^2 x=\frac{23}{2} \\ & \therefore \sinh 2 x+\cosh 2 x=\frac{23+5…