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

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

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2*sin(x)=sin(2x)

2 \cdot sin (x) = sin (2 x)

x = 2 πn, x = π + 2 πn

Solution steps

2 sin (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

2 sin (x) - sin (2 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 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

tan (x) = 0.4627

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

x, - y^{2} - cos (x) = 0

cos (θ) = \frac{6}{16}

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