Question

sin 2x - sin 3x = 0 ,find general solutions​

Answer 1

Sin2x - Sin3x =0
2Cos(5x/2)Sin(x/2) = 0

We can form 2 cases:

1) cos(5x/2) = 0
So, 5x/2 = (2n+1)pi/2
x = (2n+1)pi/5

2) sin(x/2) = 0
So, x/2 = npi
x= 2npi

So the general solutions are x = (2n+1)pi/5 or x = 2npi although the case of x = 2npi is already considered in x=(2n+1)pi/5 So we can say that the general solution is x = (2n+1)pi/5

Hope it helps

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