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= pi/3+2pin,t=(5pi)/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{π}{3} + 2 πn, t = \frac{5 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{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

sin (X) = 0

3 sec (x) = - 6

x, cos (x + x y) = 2

tan (a) = - 1

cos^{2} (x) + 2 cos (x) = - 1

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= pi/3+2pin,t=(5pi)/3+2pin