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MHT CET · Maths · Inverse Trigonometric Functions

\(\tan ^{-1} 2+\tan ^{-1} 3=\)

  1. A \(\frac{5 \pi}{4}\)
  2. B \(\frac{\pi}{4}\)
  3. C \(-\frac{\pi}{4}\)
  4. D \(\frac{3 \pi}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3 \pi}{4}\)

Step-by-step Solution

Detailed explanation

\(\tan ^{-1} 2+\tan ^{-1} 3=\pi+\tan ^{-1}\left(\frac{2+3}{1-2 \times 3}\right)=\pi+\) \(\tan ^{-1}\left(\frac{5}{-5}\right) \)
\( =\pi+\tan ^{-1}(-1)=\pi-\frac{\pi}{4}=\frac{3 \pi}{4}\)