Question

If `2sin^2x - cosx =1` how do you solve for x?

Answer 1

Solve `2sin^2 x - cos x = 1`

Ans: 0, `2pi`, `+- (2pi)/3`

Explanation:

Replace in the equation `sin^2 x` by `( 1- cos^2 x)`:
`2(1 - cos^2 x) - cos x - 1 = 0`
`2 - 2cos^2 x - cos x -1 = 0.`
Solve the quadratic equation in cos x.
`-2cos^2 x - cos x + 1 = 0.`
Since (a - b + c = 0), use shortcut -->
--> cos x = 1 and `cos x = c/a = -1/2`
a. cos x = 1 --> arc x = 0 and `x = 2pi`
b. `cos x = -1/2` --> arc `x = +- (2pi)/3`