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