Solveeit Logo
Login

Question

Mathematics Question on Properties of Inverse Trigonometric Functions

The value of tan−1(34)+tan−1(17)tan^{-1}\left(\frac{3}{4}\right)+ tan^{-1}\left(\frac{1}{7}\right) is

A

π\pi

B

π2\frac{\pi}{2}

C

3π4\frac{3\pi}{4}

D

π4\frac{\pi}{4}

Answer

π4\frac{\pi}{4}

Explanation

Solution

tan−1(34)+tan−1(17)tan^{-1}\left(\frac{3}{4}\right)+ tan^{-1}\left(\frac{1}{7}\right) =tan−1(34+171−34⋅17)= tan^{-1} \left(\frac{\frac{3}{4}+\frac{1}{7}}{1-\frac{3}{4}\cdot \frac{1}{7}}\right) =π4= \frac{\pi}{4}