What is the general solution for 3sin(2x)=6sin(x) ?

The general solution for 3sin(2x)=6sin(x) is x=2pin,x=pi+2pin

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3sin(2x)=6sin(x)

3 sin (2 x) = 6 sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

3 sin (2 x) = 6 sin (x)

Subtract

6 sin (x)

from both sides

3 sin (2 x) - 6 sin (x) = 0

Rewrite using trig identities

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

Factor

- 6 sin (x) + 6 cos (x) sin (x) : 6 sin (x) (cos (x) - 1)

6 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 (x) = \frac{1}{3} \cdot cos (x)

2 sin^{2} (x) - 1 = cos (x), 0 \leq x \leq 2 π

x, cos (3 y) = tan (2 x)

x, cos (x) = - \frac{26}{26}

6 cot (x) + 5 = - 1

What is the general solution for 3sin(2x)=6sin(x) ?
The general solution for 3sin(2x)=6sin(x) is x=2pin,x=pi+2pin