ExamBro
ExamBro
AP EAMCET · Maths · Inverse Trigonometric Functions

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

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

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { Since, } \tan ^{-1} 2+\tan ^{-1}(3) \\ = & \pi+\tan ^{-1}\left(\frac{2+3}{1-2 \times 3}\right)=\pi+\tan ^{-1}\left(\frac{5}{-5}\right)\end{aligned}\) \(=\pi+\tan ^{-1}(-1)=\pi-\frac{\pi}{4}=\frac{3 \pi}{4}\)