SOLUTION: show that cos(2arcsinx)=1-2x2

Algebra ->  Trigonometry-basics -> SOLUTION: show that cos(2arcsinx)=1-2x2      Log On


   

Question 770261: show that cos(2arcsinx)=1-2x2
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
using double angle formulas we write:
cos%282theta%29=1-2sin%5E2%28theta%29%0D%0A%0D%0A
with
theta=arcsin%28x%29

then we notice:
sin%28theta%29=sin%28arcsin%28x%29%29=x

and therefore
cos%282arcsinx%29=cos%282theta%29=1-2sin%5E2%28theta%29=1-2x%5E2%0D%0A%0D%0A


:)