SOLUTION: Find each value without using the calculator and please show the steps. Thank you. tan (sin^-1 1 - cos^-1 (1/2))

Algebra ->  Finance -> SOLUTION: Find each value without using the calculator and please show the steps. Thank you. tan (sin^-1 1 - cos^-1 (1/2))      Log On


   



Question 1050146: Find each value without using the calculator and please show the steps. Thank you.
tan (sin^-1 1 - cos^-1 (1/2))

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find each value without using the calculator and please show the steps. Thank you.
tan (sin^-1 1 - cos^-1 (1/2))
~~~~~~~~~~~~~~~~~~~~~~~

What is written here, is this


tan%28arcsin%281%29+-+arccos%281%2F2%29%29.


arcsin%281%29 = pi%2F2            ( because sin%28pi%2F2%29 = 1. )


arccos%281%2F2%29 = pi%2F3          ( because cos%28pi%2F3%29 = 1%2F2. )


Therefore, the original expression is


tan%28pi%2F2-pi%2F3%29 = tan%28pi%2F6%29 = sqrt%283%29%2F3.


Answer.  sqrt%283%29%2F3.