Solveeit Logo
Login

Question

Mathematics Question on Properties of Inverse Trigonometric Functions

The value of tan⁡−112+tan⁡−113+tan⁡−178\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{7}{8} is

A

tan⁡−178\tan^{-1}\frac{7}{8}

B

cot⁡−1 15\cot^{-1}\,15

C

tan⁡−1 15\tan ^{-1}\,15

D

tan⁡−12524\tan^{-1}\frac{25}{24}

Answer

tan⁡−1 15\tan ^{-1}\,15

Explanation

Solution

Now, tan−1(12)+tan−1(13)+tan−178tan^{-1}\left(\frac{1}{2}\right)+tan^{-1}\left(\frac{1}{3}\right)+tan^{-1} \frac{7}{8} =tan−1(12+131−12⋅13)+tan−178= tan^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\cdot\frac{1}{3}}\right)+tan^{-1} \frac{7}{8} =tan−1(5/65/6)+tan−178=tan−1(1)+tan−178 = tan^{-1} \left( \frac{5/6}{ 5/6}\right)+tan^{-1} \frac{7}{8} = tan^{-1}\left(1\right)+tan^{-1} \frac{7}{8} =tan−1(1+781−78) = tan^{-1} \left(\frac{1+\frac{7}{8}}{1-\frac{7}{8}}\right) =tan−1(15)= tan^{-1} \left(15\right)