tan(x)= 1/(sec(x))

Solución

tan (x) = \frac{1}{sec ( x )}

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Pasos de solución

tan (x) = \frac{1}{sec ( x )}

Restar

\frac{1}{sec ( x )}

de ambos lados

tan (x) - \frac{1}{sec ( x )} = 0

Simplificar

tan (x) - \frac{1}{sec ( x )} : \frac{tan ( x ) sec ( x ) - 1}{sec ( x )}

\frac{tan ( x ) sec ( x ) - 1}{sec ( x )} = 0

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

tan (x) sec (x) - 1 = 0

Expresar con seno, coseno

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

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

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

Re-escribir usando identidades trigonométricas

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

Usando el método de sustitución

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

sin (x) = \frac{- 1 + 5}{2} : x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

sin (x) = \frac{- 1 - 5}{2} :

Sin solución

Combinar toda las soluciones

x = arcsin (\frac{- 1 + 5}{2}) + 2 πn, x = π - arcsin (\frac{- 1 + 5}{2}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

2 \cdot cos (2 x) - 1 = 0

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

cos (θ) + 2 = 0

2 sec (x) = 2 tan (x) + 3 sec (x)

4 cos (x) + 3 sin (x) = 5