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

The general solution for sin(x)=2sin(x)cos(x) is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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sin(x)=2sin(x)cos(x)

sin (x) = 2 sin (x) cos (x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

sin (x) = 2 sin (x) cos (x)

Subtract

2 sin (x) cos (x)

from both sides

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

Factor

sin (x) - 2 sin (x) cos (x) : - sin (x) (2 cos (x) - 1)

- sin (x) (2 cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

4 sin^{3} (x) + 2 sin^{2} (x) - 2 sin (x) - 1 = 0

3 tan^{2} (θ) = 7 sec (θ) - 5

sin (x^{2} + 1) - cos (x^{2} + 1) = 0

cos (θ) = \frac{2}{3}

sin (8 x) = 0

What is the general solution for sin(x)=2sin(x)cos(x) ?
The general solution for sin(x)=2sin(x)cos(x) is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin