Solve X from trig function

[peblez]

3 sin 2 x - cos x = 0


Solve for x


i did 6 sin x cos x - cos x = 0

6 sin x = 0

sin x = 0

x = pi/2, 3/2 pi

but answer has two other values for x

i do not know why

 

[morson]

No, 6sinx \(\displaystyle \not=\\) 0.

\(\displaystyle 6sinxcosx - cosx = 0\)

\(\displaystyle cosx(6sinx - 1) = 0\)

Either \(\displaystyle cosx = 0\) or \(\displaystyle 6sinx - 1 = 0\)

This equation seems to imply an infinite number of solutions, also.

 

[peblez]

thank you for your help . appreciate it