TS EAMCET · Maths · Properties of Triangles
If \(\sin \mathrm{h} x=\frac{-1}{2}\) then \(\tan \mathrm{h} 2 x=\)
- A \(\frac{-\sqrt{5}}{2}\)
- B \(-\sqrt{3}\)
- C \(\frac{-\sqrt{5}}{3}\)
- D \(\frac{-\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{-\sqrt{5}}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given } \sin \mathrm{h} x=-\frac{1}{2} \\ & \cos ^2 \mathrm{~h} x-\sin ^2 \mathrm{~h} x=1 \\ & \cos ^2 h x=1+\frac{1}{4}=\frac{5}{4} \\ & \cosh x=\frac{\sqrt{5}}{2} \\ & \tanh x=\frac{\sinh x}{\cos \mathrm{h}…
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