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

Solución

tan (x - π) - 2 sin (x - π) = 0

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

Pasos de solución

tan (x - π) - 2 sin (x - π) = 0

Re-escribir usando identidades trigonométricas

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

Simplificar

\frac{sin ( x )}{cos ( x )} + 2 sin (x) : \frac{sin ( x ) + 2 sin ( x ) cos ( x )}{cos ( x )}

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

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

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

Factorizar

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

Combinar toda las soluciones

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

sin (y) = - \frac{1}{2}

cos^{22} (x) - 2 sin^{2} (x) - 1 = 0

tan (θ) = \frac{3 5}{2}

sin (x + \frac{π}{2}) + cos^{2} (x) = 0

3 sin^{2} (x) - sin (x) - 4 = 0