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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

- 2 sin (x)

from both sides

- 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

sin (8 x + 2) = cos (6 x - 10)

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ \leq 2 π

sin^{2} (2 x) = 2 sin^{2} (x)

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

\frac{3}{2} = sin (arcsin (0) + c_{1})

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