What is the general solution for 3sin(x)-2sin(x)cos(x)=0 ?

The general solution for 3sin(x)-2sin(x)cos(x)=0 is x=2pin,x=pi+2pin

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3sin(x)-2sin(x)cos(x)=0

3 sin (x) - 2 sin (x) cos (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

3 sin (x) - 2 sin (x) cos (x) = 0

Factor

3 sin (x) - 2 sin (x) cos (x) : - sin (x) (2 cos (x) - 3)

- sin (x) (2 cos (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 3 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

8 tan (b) + 12 = 3 tan (b) + 7

sin (θ) + 2 = - sin (θ)

cos (x) = π

3 cot (θ) + 1 = 0

- cos (x) + sin (x) = 0

What is the general solution for 3sin(x)-2sin(x)cos(x)=0 ?
The general solution for 3sin(x)-2sin(x)cos(x)=0 is x=2pin,x=pi+2pin