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desarrollar sec(pi(x-1))-sec(pix)

Solución

desarrollar

sec (π (x - 1)) - sec (π x)

- 2 sec (π x)

Pasos de solución

sec (π (x - 1)) - sec (π x)

sec (π (x - 1)) = - \frac{1}{cos ( π x )}

= - \frac{1}{cos ( π x )} - sec (π x)

Convertir a fracción:

sec (π x) = \frac{sec ( π x ) cos ( π x )}{cos ( π x )}

= - \frac{1}{cos ( π x )} - \frac{sec ( π x ) cos ( π x )}{cos ( π x )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 1 - sec ( π x ) cos ( π x )}{cos ( π x )}

Expresar con seno, coseno

= \frac{- 1 - 1}{cos ( π x )}

Restar:

- 1 - 1 = - 2

= \frac{- 2}{cos ( π x )}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{cos ( π x )}

Utilizar la identidad trigonométrica básica:

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

= - 2 sec (π x)

\frac{π ( 9 \cdot 3 ^{\frac{2}{3}} - 3 )}{5}

(y = 17 - 2 x) \cdot (9 - 2 x) \cdot (x)

- (\frac{( x ^{2} + 1 )}{( x ^{2} - 1 ) ^{2}})

A (2, - 2) B (8, 1)

- \frac{2 ( 4 2 - 5 )}{7}