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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

3 arcsin (x) = π

6 sec (θ) + 8 = - 4

cos^{2} (θ) - cos (θ) - 2 = 0

2 sin (3 x) = - 1

8 sin^{2} (θ) + 2 sin (θ) - 1 = 0

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