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

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

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

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

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

Solution steps

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

Subtract

2 sin (x)

from both sides

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

Rewrite using trig identities

- 2 sin (x) + 4 cos (x) sin (x) = 0

Factor

- 2 sin (x) + 4 cos (x) sin (x) : 2 sin (x) (2 cos (x) - 1)

2 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

tan (x) = \frac{1}{7}

cos^{2} (x) = 0.1

cos (x) = 0.184

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

(10 cos (2 t + \frac{π}{6})) = 0

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