Question

$Ifta{n}^{-1}\left(a\right)=\frac{\pi }{4}thenfindta{n}^{-1}(-a).$

• A. $\frac{\pi }{4}$
• B. $\frac{-\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{-\pi }{3}$

Answer 1

The correct option is B $\frac{-\pi }{4}$

We know that f(x) = $ta{n}^{-1}\left(x\right)$ is an odd funtion. Then from the property of odd functions we can say
$f(-x)=-f\left(x\right)orta{n}^{-1}(-x)=-ta{n}^{-1}\left(x\right)ta{n}^{-1}\left(x\right)=\frac{\pi }{4}\left(Given\right)ta{n}^{-1}(-x)=-ta{n}^{-1}\left(x\right)=-\frac{\pi }{4}$