-sin(x/2)+sin(x)=0

Solución

- sin (\frac{x}{2}) + sin (x) = 0

x = \frac{2 π}{3} + \frac{8 πn}{3}, x = 2 π + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

Pasos de solución

- sin (\frac{x}{2}) + sin (x) = 0

Re-escribir usando identidades trigonométricas

2 cos (\frac{3 x}{4}) sin (\frac{x}{4}) = 0

Resolver cada parte por separado

cos (\frac{3 x}{4}) = 0 or sin (\frac{x}{4}) = 0

cos (\frac{3 x}{4}) = 0 : x = \frac{2 π}{3} + \frac{8 πn}{3}, x = 2 π + \frac{8 πn}{3}

sin (\frac{x}{4}) = 0 : x = 8 πn, x = 4 π + 8 πn

Combinar toda las soluciones

x = \frac{2 π}{3} + \frac{8 πn}{3}, x = 2 π + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

3 sin (2 θ) = 2 cos (2 θ)

cos (x) + cos^{2} (x) = 0

cos (θ) = cos (1)

tan (\frac{x}{2}) = \pm \frac{1 - cos ( x )}{1 + cos ( x )}

sin^{2} (x) - cos^{2} (x) = 0.5