1. Solving sin(pi/3-2x) = sin(x-pi/6)

Hi!

Having problems getting correct answers for the equation
$\displaystyle sin(pi/3-2x) = sin(x-pi/6)$

Could someone help and point me to the right direction with this one ?

Thanks!

2. Hello thex10

Welcome to Math Help Forum!
Originally Posted by thex10
Hi!

Having problems getting correct answers for the equation
$\displaystyle sin(pi/3-2x) = sin(x-pi/6)$

Could someone help and point me to the right direction with this one ?

Thanks!
The general solution of the equation:
$\displaystyle \sin A = \sin B$
is:
$\displaystyle A = n\pi + (-1)^nB, n = 0 , \pm 1, \pm 2, ...$
So for instance,
When $\displaystyle n = 0,\; A = B$

When $\displaystyle n = 1,\; A = \pi - B$

When $\displaystyle n = 2,\; A = 2\pi + B$

... and so on

So to solve the equation
$\displaystyle \sin(\pi/3-2x) = \sin(x-\pi/6)$
you first write down the general solution, as above, where
$\displaystyle A = \pi/3 - 2x$
and
$\displaystyle B = x - \pi/6$
which is:
$\displaystyle \pi/3 - 2x =n\pi +(-1)^n(x - \pi/6)$
and then see what happens when you take particular values for $\displaystyle n$.

Can you continue from here?