```Question 413727
sin(2x) = -2sin(x)
First let's use the sin(2x) formula so we have everything in terms of just x:
2sin(x)cos(x) = -2sin(x)
Now we'll add 2sin(x) to each side:
2sin(x)cos(x) + 2sin(x) = 0
And then factor out the GCF which is 2sin(x):
2sin(x)(cos(x) + 1) = 0
From the Zero Product Property we know that one of these factors must be zero. So:
2sin(x) = 0 or cos(x) + 1 = 0
Dividing the first equation by 2 and subtracting 1 from the second equation we get:
sin(x) = 0 or cos(x) = -1
So the solutions will by any value for x that makes the sin zero or the cos -1. If you know your special angles you know that 0, {{{pi}}} and any angle coterminal with them will make sin zero. And {{{pi}}} and any angle coterminal with it will make cos -1. To express this algebraically we use:
x = 0 + 2{{{pi}}}n
or
x = {{{pi}}} + 2{{{pi}}}n
where "n" is any integer. (This is how we include "all the angles coterminal with...") (We only need one equation for the angles that are coterminal with {{{pi}}}. If you don't know what a radian is or if you want an answer in degrees then change the {{{pi}}} to 180 and the 2{{{pi}}} to 360.```