Question 1050146
.
Find each value without using the calculator and please show the steps. Thank you.

tan (sin^-1 1 - cos^-1 (1/2))
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
What is written here, is this


{{{tan(arcsin(1) - arccos(1/2))}}}.


{{{arcsin(1)}}} = {{{pi/2}}}            ( because {{{sin(pi/2)}}} = 1. )


{{{arccos(1/2)}}} = {{{pi/3}}}          ( because {{{cos(pi/3)}}} = {{{1/2}}}. )


Therefore, the original expression is


{{{tan(pi/2-pi/3)}}} = {{{tan(pi/6)}}} = {{{sqrt(3)/3}}}.


<U>Answer</U>.  {{{sqrt(3)/3}}}.
</pre>