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

1 Answer
Alan P.
Feb 14, 2015

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

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
22402 views around the world
You can reuse this answer
Creative Commons License