Question

$co{t}^{-1}\left(0.2\right)=c,thenfindta{n}^{-1}(-5).$

• A. - c
• B. 2c
• C. $\frac{c}{2}$
• D. None of these

Answer 1

The correct option is A - c

Well, in this problem we will be using two properties.
$Weknowco{t}^{-1}\left(x\right)=ta{n}^{-1}\left(\frac{1}{x}\right)co{t}^{-1}\left(0.2\right)=ta{n}^{-1}\left(\frac{1}{0.2}\right)=ta{n}^{-1}\left(5\right)So,ta{n}^{-1}\left(5\right)=cButweareaskedtofindta{n}^{-1}\left(5\right)$
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 -
$ta{n}^{-1}(-x)=-ta{n}^{-1}\left(x\right)(Since,ta{n}^{-1}(x\left)isanoddfunction\right)So,ta{n}^{-1}(-5)=-ta{n}^{-1}\left(5\right)=-c$