(2sin^2(x)-1)(3tan^2(x)-1)=0

Solución

(2 sin^{2} (x) - 1) (3 tan^{2} (x) - 1) = 0

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

Pasos de solución

(2 sin^{2} (x) - 1) (3 tan^{2} (x) - 1) = 0

Resolver cada parte por separado

2 sin^{2} (x) - 1 = 0 or 3 tan^{2} (x) - 1 = 0

2 sin^{2} (x) - 1 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

3 tan^{2} (x) - 1 = 0 : x = arctan (\frac{1}{3}) + πn, x = arctan (- \frac{1}{3}) + πn

Combinar toda las soluciones

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = arctan (\frac{1}{3}) + πn, x = arctan (- \frac{1}{3}) + πn

Mostrar soluciones en forma decimal

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = 0.52359 \dots + πn, x = - 0.52359 \dots + πn

sec (x) - 1 = 0

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

csc (θ) = - 2

3 cos (2 t) + 4 = 1

sin^{2} (x) = 4 - 2 cos^{2} (x)