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

Solución

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

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

Pasos de solución

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

Restar

1 - sin^{2} (x)

de ambos lados

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

Re-escribir usando identidades trigonométricas

- 1 + sec^{2} (x) sin^{2} (x) = 0

Factorizar

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

(sec (x) sin (x) + 1) (sec (x) sin (x) - 1) = 0

Resolver cada parte por separado

sec (x) sin (x) + 1 = 0 or sec (x) sin (x) - 1 = 0

sec (x) sin (x) + 1 = 0 : x = \frac{3 π}{4} + πn

sec (x) sin (x) - 1 = 0 : x = \frac{π}{4} + πn

Combinar toda las soluciones

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

2 sin^{2} (x) = 3 - 5 cos (x)

- 3 cos (2 θ) - 18 sin (θ) - 8 = - 5 sin (θ) - 6

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

tan^{2} (x) + 4 tan (x) = 3

sin (1 - 2 x) = 1