MHT CET · Maths · Inverse Trigonometric Functions
\(2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\)
- A \(\frac{\pi}{4}\)
- B \(0\)
- C \(\tan ^{-1}\left(\frac{5}{4}\right)\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(2 \tan ^{-1}\left(\frac{1}{3}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\tan ^{-1} \frac{2 \times \frac{1}{3}}{1-\left(\frac{1}{3}\right)^2}+\cos ^{-1}\) \(\left(\frac{3}{5}\right) \)
\( =\tan ^{-1}\left(\frac{\frac{2}{3}}{\frac{8}{9}}\right)+\cos ^{-1}\left(\frac{3}{5}\right) \)
\( =\tan ^{-1}\left(\frac{3}{4}\right)+\cot ^{-1}\left(\frac{3}{4}\right) \)
\( =\frac{\pi}{2}\)
\( =\tan ^{-1}\left(\frac{\frac{2}{3}}{\frac{8}{9}}\right)+\cos ^{-1}\left(\frac{3}{5}\right) \)
\( =\tan ^{-1}\left(\frac{3}{4}\right)+\cot ^{-1}\left(\frac{3}{4}\right) \)
\( =\frac{\pi}{2}\)
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