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

The general solution for -sin(x)-2sin(2x)=0 is x=2pin,x=pi+2pin,x=1.82347…+2pin,x=-1.82347…+2pin

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

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

x = 2 πn, x = π + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Factor

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

- sin (x) (4 cos (x) + 1) = 0

Solving each part separately

sin (x) = 0 or 4 cos (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos (x) + 1 = 0 : x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

sin (\frac{π}{6} - x) = 1

t, F = 4 cos (- 2 t + 7) + C

c, 2 = 4 sin (0.5 (0 - c)) + 2

3 cos^{2} (x) - 23 cos (x) = cos (x)

196 sin (θ) - 49 cos (θ) = 160

What is the general solution for -sin(x)-2sin(2x)=0 ?
The general solution for -sin(x)-2sin(2x)=0 is x=2pin,x=pi+2pin,x=1.82347…+2pin,x=-1.82347…+2pin