sin x – 2sin x cos x = 0

Question

Help please

Answer 1

Factor sin x out of both terms on the left:

 

sin x – 2sin x cos x = 0

sin x (1 - 2cos x) = 0

 

Just as you've seen when solving quadratic equations by factoring, if two or more factors multiplied by each other are 0, then one of the factors is 0.

 

So either sin x = 0, or 1 - 2cos x = 0

 

If sin x = 0, then x = 2πN, where N can be any integer.

 

If 1 - 2cos x = 0, then...

 

1 = 2 cos x

1/2 = cos x

x = π/3 + 2πN, or x = 5π/3 + 2πN

 

So the solutions are x = 2πN, x = π/3 + 2πN, or x = 5π/3 + 2πN.