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

The general solution for sin(2t)=sin(t) is t=2pin,t=pi+2pin,t= pi/3+2pin,t=(5pi)/3+2pin

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sin(2t)=sin(t)

sin (2 t) = sin (t)

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)

Subtract

sin (t)

from both sides

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

cos (x) = \frac{17.6}{26}

tan (2 θ) = - 2.5

1 + 4 cos (θ) = 3 sin (θ), 0 \leq θ \leq 2 π

\frac{150}{sin ( x )} = \frac{140.78}{sin ( 11 5 ^{\circ} )}

tan^{2} (x) + cot^{2} (x) = 2

What is the general solution for sin(2t)=sin(t) ?
The general solution for sin(2t)=sin(t) is t=2pin,t=pi+2pin,t= pi/3+2pin,t=(5pi)/3+2pin