tan(x)=2sin(x)

Solución

tan (x) = 2 sin (x)

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

Pasos de solución

tan (x) = 2 sin (x)

Restar

2 sin (x)

de ambos lados

tan (x) - 2 sin (x) = 0

Expresar con seno, coseno

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factorizar

sin (x) - 2 cos (x) sin (x) : - sin (x) (2 cos (x) - 1)

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

Resolver cada parte por separado

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combinar toda las soluciones

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

3 csc (x) = 2

tan^{2} (x) + tan (x) - 12 = 0

sin (x) + 1 = cos (x)

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

sec^{2} (x) = 0