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Question

Mathematics Question on Inverse Trigonometric Functions

If $?

A

00

B

11

C

π4\frac{\pi}{4}

D

π6\frac{\pi}{6}

Answer

π4\frac{\pi}{4}

Explanation

Solution

We have, ABCABC is a right angled Δ\Delta at AA ⇒  a2=b2+c2…(i)\Rightarrow\,\,a^{2} = b^{2} + c^{2}\quad\ldots\left(i\right) Now, tan−1(ca+b)+tan−1(ba+c)tan^{-1}\left(\frac{c}{a + b}\right) + tan^{-1} \left(\frac{b}{a + c}\right) = tan^{-1}\left\\{\frac{\left(\frac{c}{a + b}\right) +\left(\frac{b}{a + c}\right)}{1-\left(\frac{c}{a + b}\right) \left(\frac{b}{a + c}\right)}\right\\} = tan^{-1}\left\\{\frac{ac+c^{2} +b^{2} +ab}{a^{2} + ab+ac}\right\\} = tan^{-1}\left\\{\frac{ac+a^{2} +ab}{a^{2} + ab+ac}\right\\}\quad using (i)\left(i\right) =tan−1(1)=π4= tan^{-1}\left(1\right) = \frac{\pi}{4}