AP EAMCET · Maths · Trigonometric Ratios & Identities
Which of the following expression is always true?
- A \(\cosh \frac{x}{2}=\sqrt{\frac{\cosh x-1}{2}}\)
- B \(\tanh \left(\frac{x}{2}\right)=\frac{2 \sinh x}{\cosh x+1}\)
- C \(\sinh \left(\frac{x}{2}\right)=\frac{\sinh x}{\sqrt{2(\cosh x+1)}}\)
- D \(\sinh \left(\frac{x}{2}\right)=\frac{\sinh x}{\sqrt{2(\cosh x-1)}}\)
Answer & Solution
Correct Answer
(C) \(\sinh \left(\frac{x}{2}\right)=\frac{\sinh x}{\sqrt{2(\cosh x+1)}}\)
Step-by-step Solution
Detailed explanation
(a) \(\cosh \frac{x}{2}=\sqrt{\frac{1+\cosh x}{2}}\) (b) \(\tanh \left(\frac{x}{2}\right)=\frac{\sinh x}{\cosh x+1}\) (c) \(\sinh \left(\frac{x}{2}\right)=\frac{\sinh x}{\sqrt{2(\cosh x+1)}}\)
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