Evaluate each expression
tan(arccos(2/2))
cos(arcsin(5/13))
Evaluate each expression
tan(arccos(2/2))
cos(arcsin(5/13))
$\displaystyle tan(arccos(\frac{\sqrt2}{2})) = tan(\frac{\pi}{4}) = 1$
what you need to notice: $\displaystyle cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
what you need to remember: $\displaystyle arccos(cos(x)) = cos^{-1}(cos(x)) = x$
$\displaystyle \therefore arccos(cos(\frac{\pi}{4})) = arccos(\frac{\sqrt{2}}{2})$
so, $\displaystyle \frac{\pi}{4} = arccos(\frac{\sqrt{2}}{2}) $
Try the second one.