tan(x+pi)+2sin(x+pi)=0,0<= x<= 2pi

Solución

tan (x + π) + 2 sin (x + π) = 0, 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

Pasos de solución

tan (x + π) + 2 sin (x + π) = 0, 0 \leq x \leq 2 π

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, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

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

Combinar toda las soluciones

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

sin (a) + 3 cos (a) = 0

22 cos (θ) + 3 = 5

sin (a) cos (a) = 1

sin (2 π x) = 0

sin (5 x) = 1