What is the general solution for sin(2t)+sin(t)=0 ?

The general solution for sin(2t)+sin(t)=0 is t=2pin,t=pi+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin

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sin(2t)+sin(t)=0

sin (2 t) + sin (t) = 0

t = 2 πn, t = π + 2 πn, t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

Solution steps

sin (2 t) + sin (t) = 0

Rewrite using trig identities

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

Factor

sin (t) + 2 cos (t) sin (t) : sin (t) (2 cos (t) + 1)

sin (t) (2 cos (t) + 1) = 0

Solving each part separately

sin (t) = 0 or 2 cos (t) + 1 = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

2 cos (t) + 1 = 0 : t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

Combine all the solutions

t = 2 πn, t = π + 2 πn, t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

2 sin^{2} (x) = 3 (cos (x) + 1)

3 cot (\frac{x}{2}) = 3

tan^{2} (θ) - 6 tan (θ) + 5 = 0

tan (4 θ) = - 1

cot (x) (tan (x) - 1) = 0

What is the general solution for sin(2t)+sin(t)=0 ?
The general solution for sin(2t)+sin(t)=0 is t=2pin,t=pi+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin