Question

If arctan(tanα) = -2π/7 Which of the following values can have α have?

a) -9π/7

b) 2π/7

c) -5π/7

d) 5π/7

Answer 1

Answer:-

arctan(x) is same as tan^-1(x)

Graph of tan^-1($x$ )

We have given $tan^{-1}tan(\alpha)=\frac{-2\pi}{7}$

According to question , we can have values of $\alpha$ as follows

(1) $y=\alpha$

(2)$y=\alpha-\pi$

(3)$y=\alpha+\pi$

We got

$\alpha=\frac{-2\pi}{7} from (1)$

$\alpha=\frac{-9\pi}{7} \ from(2)$

$\alpha=\frac{5\pi}{7} \ from (3)$

So , in the given question options (a) and (d) are possible.