Posted by Abby on Saturday, February 20, 2010 at 12:54pm.
Find all the solutions of the equation in the interval (0,2pip)
sin(x + pi/6)  sin(x pi/6) = 1/2
I am only stuck on the last part. I have 2sinx(sqrt3/2) = 1/2 Does the 2 cancel out with the sqrt 3/2. I am not sure what to do.

PreCal(Urgent!!)  Reiny, Saturday, February 20, 2010 at 1:09pm
I don't see how you got 2sinx(sqrt3/2) = 1/2 .
Here is what I would do:
sin(x + pi/6)  sin(x pi/6) = 1/2
sinxcospi/6 + cosxsinpi/6  (sinxcospi/6  cosxsinpi/6) = 1/2
2cosxsinpi/6 = 1/2
cosx = 1/2, since sinpi/6 = 1/2
so x is in the first or fourth quadrants
In quad I, x = pi/3 , (60 degrees) or
in quad IV, x = 2pi  pi/6 = 11pi/6 , (300 degrees)
BTW, if 2sinx(sqrt3/2) = 1/2 were correct,
you could NOT cancel the 2's 
PreCal(Urgent!!)  drwls, Saturday, February 20, 2010 at 1:15pm
You got a sign wrong somewhere.
Using the sin (a+b) and sin (ab) formulas, the left half becomes
sinx cos pi/6 + sin(pi/6) cosx
 sinx cos(pi/6) + cosx sin(pi/6) = 1/2
2 cosx sin pi/6 = 1/2
cos x = 1/2
x = pi/3 or 5 pi/3 
PreCal(Urgent!!)  drwls, Saturday, February 20, 2010 at 1:16pm
I agree with Reiny up until the 11 pi/6

PreCal(Urgent!!)  Reiny, Saturday, February 20, 2010 at 3:26pm
Yup, drwls is right,
I should have had 2pi  pi/3,
x = 5pi/3,
(I had 2pi  pi/6, don't know where that came from)