Question

If $co{t}^{-1}\left(0.2\right)=c,then{\tan }^{-1}(-5)=$

• A. $-c$
• B. $2c$
• C. $\frac{c}{2}$
• D. $c$

Answer 1

The correct option is A $-c$

In this problem we will be using two properties.
$Weknowco{t}^{-1}\left(x\right)=ta{n}^{-1}\left(\frac{1}{x}\right)co{t}^{-1}\left(0.2\right)=ta{n}^{-1}\left(\frac{1}{0.2}\right)=ta{n}^{-1}\left(5\right)So,ta{n}^{-1}\left(5\right)=cButweareaskedtofindta{n}^{-1}(-5)$
We know one more property of inverse trigonometric functions. Well, this is not just the property of inverse trigonometric functions. This is the property of odd functions according to which
${\tan }^{-1}(-x)=-{\tan }^{-1}x$ (Since, ${\tan }^{-1}x$ is an odd function)
So, ${\tan }^{-1}(-5)=-{\tan }^{-1}\left(5\right)=-c$