Question

How do you solve for x in `4sinxcosx+2sinx-2cosx-1=0`?

Answer 1

`x in {30^@, 120^@, 150^@, 240^@}`
`color(white)("XXX")+- "any integer multiple of " 360^@`

Explanation:

Factor `4 sin x cos x + 2sin x − 2cos x − 1 = 0`
as
`(2 sin(x) - 1) (2 cos(x) + 1) = 0`
then solve the two terms using standard trig values.

`2 sin(x) - 1 = 0`
`rarr` `sin(x) = 1/2`
`rarr` `x = 30^o` or `x = 150^o`

or
`2 cos(x) + 1 = 0`
`rarr` `cos(x) = (-1)/2`
`rarr` `x = 120^o` or `x = 240^o`