(sin(2x)}{sin(\frac{7pi)/2-x)}=sqrt(2)

Solución

\frac{sin ( 2 x )}{sin ( \frac{7 π}{2} - x )} = 2

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Pasos de solución

\frac{sin ( 2 x )}{sin ( \frac{7 π}{2} - x )} = 2

Re-escribir usando identidades trigonométricas

- \frac{sin ( 2 x )}{cos ( x )} = 2

Restar

2

de ambos lados

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

Simplificar

- \frac{sin ( 2 x )}{cos ( x )} - 2 : \frac{- sin ( 2 x ) - 2 cos ( x )}{cos ( x )}

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

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

- sin (2 x) - 2 cos (x) = 0

Re-escribir usando identidades trigonométricas

- cos (x) 2 - 2 cos (x) sin (x) = 0

Factorizar

- cos (x) 2 - 2 cos (x) sin (x) : - cos (x) (2 + 2 sin (x))

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

Resolver cada parte por separado

cos (x) = 0 or 2 + 2 sin (x) = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

Combinar toda las soluciones

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

Siendo que la ecuación esta indefinida para:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

- 2 sec (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

cos (x + 1) = - \frac{2}{5}

4 cos (2 x) + 1 = 3

sinh^{2} (x) = 0

cos (x) csc^{2} (x) + 3 cos (x) = 7 cos (x)