How do you evaluate tan(tan^-1(135))?

Aug 22, 2016

135

Explanation:

${\tan}^{-} 1$ 135 means the angle whose tan is 135.

If we think about an angle whose tan we know:
Draw a right angled isosceles triangle.
The tan of a 45 degree angle is 1
So ${\tan}^{-} 1$(1) =45

Tan(45)=1
So instead of 45 I can write ${\tan}^{-} 1 \left(1\right)$

Tan( ${\tan}^{-} 1 \left(1\right)$)= 1

Likewise tan(${\tan}^{-} 1 \left(135\right)$)=135