sin(x)cos(x)+sin(x)=3cos^2(x)+3cos(x)

Solución

sin (x) cos (x) + sin (x) = 3 cos^{2} (x) + 3 cos (x)

x = π + 2 πn, x = 1.24904 \dots + πn

Pasos de solución

sin (x) cos (x) + sin (x) = 3 cos^{2} (x) + 3 cos (x)

Restar

3 cos^{2} (x) + 3 cos (x)

de ambos lados

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

Factorizar

sin (x) cos (x) + sin (x) - 3 cos^{2} (x) - 3 cos (x) : (cos (x) + 1) (sin (x) - 3 cos (x))

(cos (x) + 1) (sin (x) - 3 cos (x)) = 0

Resolver cada parte por separado

cos (x) + 1 = 0 or sin (x) - 3 cos (x) = 0

cos (x) + 1 = 0 : x = π + 2 πn

sin (x) - 3 cos (x) = 0 : x = arctan (3) + πn

Combinar toda las soluciones

x = π + 2 πn, x = arctan (3) + πn

Mostrar soluciones en forma decimal

x = π + 2 πn, x = 1.24904 \dots + πn

2 - 2 sin^{2} (x) = - 3 cos (x) + 2

4 tan (θ) + 7 = 0

arctan (x) + arctan (3 x) + arctan (7 x) = 18 0^{\circ}

2 cos (a) = 1

cos^{2} (x) = (\frac{1}{2})