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

Solución

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

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Pasos de solución

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

Restar

2

de ambos lados

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

Re-escribir usando identidades trigonométricas

- 1 + 2 cos (2 x) = 0

Mover

1

al lado derecho

2 cos (2 x) = 1

Dividir ambos lados entre

2

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

Soluciones generales para

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

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

Resolver

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Resolver

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

x, cos (3 x) = 1

sec (x) + tan (x) = 2

\frac{1}{cos ^{2} ( x )} = \frac{4}{3}

cos (A) = - \frac{1}{2}

sin (x) = cos (4 x)