Expert: Steve Holleran - 4/3/2008

Question
Find all solutions to the equation:

2cosXsinX-sinX

Answer
Hi Shyann,

There's no equation here, because you haven't set it equal to anything, but I'm going to assume its =0.

If so, then you have:

   2 cos x sin x - sin x = 0

   sin x (2 cos x - 1) = 0

so  sin x = 0   or 2 cos x - 1 = 0

Sin x = 0 at x = 0 and pi, so x = 0 +/- k*pi

2 cos x - 1 = 0 --> 2 cos x = 1 --->  cos x = 1/2

and this occurs at x = pi/3 and 5pi/3, so say

x = pi/3 +/- 2k * pi

x = 5pi/3 +/- 2k * pi


Steve