Question

Solve for x where...


`cos(2x) - sin(x) = 0`

Answer 1

use double angle identity:

`cos (2x) = 1-2sin^2 (x)`
After substituting and moving to Right side of equation:

`2 sin^2 (x) + sin (x) -1 = 0`
This is a quadratic, which can be solved by factoring or quadratic formula.
It may be helpful to replace sin(x) with another variable, then solve.

`u = sin(x) \\ 2u^2 +u-1=0 \\ (2u-1)(u+1) = 0 \\ u = (1)/(2) , -1`
Now substitute sin(x) back in, we have

`sin (x) = (1)/(2), -1`
Using a unit circle or inverse sine function in calculator we can find the appropriate angles.

`x = (\pi)/(6), (3\pi)/(2)`