SOLUTION: Rewrite the equation {{{ sin2x=cos(x) }}} using only cos(x) (and numbers). Then find all solutions to the equation. Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite the equation {{{ sin2x=cos(x) }}} using only cos(x) (and numbers). Then find all solutions to the equation. Thanks!      Log On


   

Question 960731: Rewrite the equation +sin2x=cos%28x%29+
using only cos(x) (and numbers). Then find all solutions to the equation.

Thanks!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite the equation +sin2x=cos%28x%29+
using only cos(x) (and numbers).
2sin*cos = cos
2%2Asqrt%281-cos%5E2%28x%29%29%2Acos%28x%29+=+cos%28x%29
==========================
Then find all solutions to the equation.
2sin*cos = cos
2sin*cos - cos = 0
cos(2sin - 1) = 0
cos = 0
x = pi + n*pi n = 0,1,2,3...
---------------
2sin - 1 = 0
sin(x) = 1/2
x = pi/6 + 2n*pi n = 0,1,2,3...
x = 5pi/6 + 2n*pi n = 0,1,2,3...