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

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

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sin(t)-sin(2t)=0

sin (t) - sin (2 t) = 0

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

Solution steps

sin (t) - sin (2 t) = 0

Rewrite using trig identities

- 2 cos (\frac{3 t}{2}) sin (\frac{t}{2}) = 0

Solving each part separately

cos (\frac{3 t}{2}) = 0 or sin (\frac{t}{2}) = 0

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

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

Combine all the solutions

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

sin (\frac{3 x}{2}) = 0

tan (x) = 5 sin (x)

cot^{2} (x) = - 2 cot (x) - 1

cos (\frac{π t}{2}) = 0

sin (θ) = - \frac{3}{7}

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