AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin \mathrm{h} x=\frac{\sqrt{21}}{2}\) then \(\cosh 2 x+\sinh 2 x=\)
- A \(\frac{21}{2}\)
- B \(\frac{25}{2}\)
- C \(\frac{23+5 \sqrt{21}}{2}\)
- D \(\frac{32+5 \sqrt{23}}{2}\)
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…
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