AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h^{-1}\left(\frac{3}{4}\right)\) equals to
- A \(\log _e(3(2+\sqrt{3}))\)
- B \(\log _e\left(\frac{1+\sqrt{3}}{3}\right)\)
- C \(\log _e\left(\frac{2+\sqrt{3}}{3}\right)\)
- D \(\log _e\left(\frac{2-\sqrt{3}}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\log _e\left(\frac{2+\sqrt{3}}{3}\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \because \sec h^{-1} x=\log _e\left(\frac{1+\sqrt{1-x^2}}{x}\right) \\ & \text { and cosec } h^{-1} x=\log _e\left(\frac{1+\sqrt{1+x^2}}{x}\right) \\ & \therefore \sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h\left(\frac{3}{4}\right) \\ & =\log…
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