2cos(2t)+2cos^2(t)=0

Solución

2 cos (2 t) + 2 cos^{2} (t) = 0

t = - 0.95531 \dots + πn, t = 0.95531 \dots + πn

Pasos de solución

2 cos (2 t) + 2 cos^{2} (t) = 0

Re-escribir usando identidades trigonométricas

- 2 sin^{2} (t) + 4 cos^{2} (t) = 0

Factorizar

- 2 sin^{2} (t) + 4 cos^{2} (t) : 2 (2 cos (t) + sin (t)) (2 cos (t) - sin (t))

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

Resolver cada parte por separado

2 cos (t) + sin (t) = 0 or 2 cos (t) - sin (t) = 0

2 cos (t) + sin (t) = 0 : t = arctan (- 2) + πn

2 cos (t) - sin (t) = 0 : t = arctan (2) + πn

Combinar toda las soluciones

t = arctan (- 2) + πn, t = arctan (2) + πn

Mostrar soluciones en forma decimal

t = - 0.95531 \dots + πn, t = 0.95531 \dots + πn

5 \cdot cos (x) + 4 - 2 \cdot sin (x) = 0

sin (x) = - 0.54

tan (2 θ) = 1.82

sin (x) = - 0.65

sin (x) = - 0.71