The value of tan − 1 2 + tan − 1 3 is, ( 4 3 π ) c, ( 2 π ) c, ( 4 π ) c, ( 6 π ) c

tan − 1 2 + tan − 1 3 = tan − 1 [ 1 − ( 2 ) ( 3 ) 2 + 3 ] = tan − 1 ( 1 − 6 5 ) = tan − 1 ( − 1 ) = ( 4 3 π ) c

The value of tan − 1 2 + tan − 1 3 is

Search any question & find its solution

Question: Answered & Verified by Expert

The value of $\tan ^{-1} 2+\tan ^{-1} 3$ is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $\left(\frac{3 \pi}{4}\right)^c$
B $\left(\frac{\pi}{2}\right)^c$
C $\left(\frac{\pi}{4}\right)^c$
D $\left(\frac{\pi}{6}\right)^c$

Solution:

2569 Upvotes Verified Answer

The correct answer is: $\left(\frac{3 \pi}{4}\right)^c$

$\begin{aligned} & \tan ^{-1} 2+\tan ^{-1} 3 \\ & =\tan ^{-1}\left[\frac{2+3}{1-(2)(3)}\right]=\tan ^{-1}\left(\frac{5}{1-6}\right)=\tan ^{-1}(-1)=\left(\frac{3 \pi}{4}\right)^c\end{aligned}$

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.

Use on iOS or Desktop Download from Google Play