sin(x)+cos(x)=sec(x)

Solución

sin (x) + cos (x) = sec (x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Pasos de solución

sin (x) + cos (x) = sec (x)

Restar

sec (x)

de ambos lados

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

Expresar con seno, coseno

\frac{- 1 + cos ^{2} ( x ) + cos ( x ) sin ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Re-escribir usando identidades trigonométricas

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

Factorizar

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

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

Resolver cada parte por separado

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

y, x = tan (y^{2})

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

sin (x) = - 0.2761

3 arcsin (x) = \frac{π}{2}, x

sin^{2} (θ) - \frac{1}{2} sin (θ) - \frac{1}{2} = 0