# How do you find the exact value of tan(cos^-1(sqrt2/2))?

Aug 23, 2016

$\tan \left\{{\cos}^{-} 1 \left(\frac{\sqrt{2}}{2}\right)\right\} = \tan \left(\frac{\pi}{4}\right) = 1$.

#### Explanation:

Recall the Defn. :-

${\cos}^{-} 1 x = \theta , | x | \le 1 \iff x = \cos \theta , \theta \in \left[0 , \pi\right]$

Knowing that, cos(pi/4)=sqrt2/2, pi/4 in [0,pi]; cos^-1(sqrt2/2)=pi/4.

Hence,

$\tan \left\{{\cos}^{-} 1 \left(\frac{\sqrt{2}}{2}\right)\right\} = \tan \left(\frac{\pi}{4}\right) = 1$.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}