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

Solución

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

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Pasos de solución

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

Factorizar

2 sin (x) cos^{2} (x) - sin (x) : sin (x) (2 cos (x) + 1) (2 cos (x) - 1)

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

Resolver cada parte por separado

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) + 1 = 0 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

tan (x) = \frac{1}{sec ( x )}

2 \cdot cos (2 x) - 1 = 0

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

cos (θ) + 2 = 0

2 sec (x) = 2 tan (x) + 3 sec (x)