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

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

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sin(2t)=2sin(t)

sin (2 t) = 2 sin (t)

t = 2 πn, t = π + 2 πn

Solution steps

sin (2 t) = 2 sin (t)

Subtract

2 sin (t)

from both sides

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

sin (t) = 0 or cos (t) - 1 = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

cos (t) - 1 = 0 : t = 2 πn

Combine all the solutions

t = 2 πn, t = π + 2 πn

cos (α) = 0

x, cos (x^{3} y^{3}) = 5 y^{3}

cos^{2} (\frac{3}{4} π + x) + sin^{2} (\frac{7}{4} π - x) = 1

sin (4 x) = - sin (x)

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

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