TS EAMCET · Maths · Trigonometric Equations
\(\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})=\)
- A \(\sinh ^{-1} 3+\cosh ^{-1}\left(\frac{1}{3}\right)\)
- B \(\cosh ^{-1} 3+\sinh ^{-1} 3\)
- C \(\tanh ^{-1} 3+\sinh ^{-1} 3\)
- D \(\cosh ^{-1} 3+\tanh ^{-1} 3\)
Answer & Solution
Correct Answer
(B) \(\cosh ^{-1} 3+\sinh ^{-1} 3\)
Step-by-step Solution
Detailed explanation
We have, \(\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})\) \(\log (9+6 \sqrt{2}+3 \sqrt{10}+4 \sqrt{5})\) \(\log (9+3 \sqrt{10}+6 \sqrt{2}+4 \sqrt{5})\) \(\log (3+\sqrt{10})(3+2 \sqrt{2})\) \(=\log (3+\sqrt{10})+\log (3+\sqrt{8})\)…
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