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

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

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3sin(x)=3sin(2x)

3 sin (x) = 3 sin (2 x)

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

Solution steps

3 sin (x) = 3 sin (2 x)

Subtract

3 sin (2 x)

from both sides

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

Rewrite using trig identities

3 sin (x) - 6 cos (x) sin (x) = 0

Factor

3 sin (x) - 6 cos (x) sin (x) : - 3 sin (x) (2 cos (x) - 1)

- 3 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

sin (x) + cos (2 x) = 0.75

sin (x) = 5 sin (x) + 2

2 sin^{2} (x) + (3 - 4) sin (x) = 23

4 cos (30 x) + 12 = 10.5

3 sin^{2} (x) + 5 cos (x) = 1

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