# SOLUTION: sin2x=-2sinx

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 Question 413727: sin2x=-2sinxAnswer by jsmallt9(3296)   (Show Source): You can put this solution on YOUR website!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, and any angle coterminal with them will make sin zero. And and any angle coterminal with it will make cos -1. To express this algebraically we use: x = 0 + 2n or x = + 2n 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 . If you don't know what a radian is or if you want an answer in degrees then change the to 180 and the 2 to 360.