Download MARKS App - Trusted by 15,00,000+ IIT JEE & NEET aspirants! Download Now
Search any question & find its solution
Question: Answered & Verified by Expert
{2}+\operatorname{coth}^{-1} 3=$
MathematicsTrigonometric EquationsAP EAMCETAP EAMCET 2018 (22 Apr Shift 1)
Options:
  • A $\log \sqrt{6}$
  • B $\log 6$
  • C $-\log \sqrt{6}$
  • D $-\log 6$
Solution:
2876 Upvotes Verified Answer
The correct answer is: $\log \sqrt{6}$
$$
\begin{aligned}
& \text {} \tanh ^{-1}\left(\frac{1}{2}\right)+\operatorname{coth} h^{-1} \text { (3) } \\
& =\frac{1}{2} \ln \left(\frac{1+\frac{1}{2}}{1-\frac{1}{2}}\right)+\frac{1}{2} \ln \left(\frac{3+1}{3-1}\right)=\frac{1}{2} \log \left(\frac{\frac{3}{2}}{\frac{1}{2}}\right)+\frac{1}{2} \log \left(\frac{4}{2}\right) \\
& =\frac{1}{2} \log 3+\frac{1}{2} \log 2 \\
& =\log \sqrt{3}+\log \sqrt{2} \\
& =\log (\sqrt{3} \cdot \sqrt{2})=\log \sqrt{6} \text {. } \\
\end{aligned}
$$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.