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Popular >

sin(-pi/(12))csc((25pi)/(12))

Solución

sin (- \frac{π}{12}) csc (\frac{25 π}{12})

- 1

Pasos de solución

sin (- \frac{π}{12}) csc (\frac{25 π}{12})

Utilizar la siguiente propiedad:

sin (- x) = - sin (x)

sin (- \frac{π}{12}) = - sin (\frac{π}{12})

= (- sin (\frac{π}{12})) csc (\frac{25 π}{12})

csc (\frac{25 π}{12}) = csc (\frac{π}{12})

csc (\frac{25 π}{12})

Reescribir

\frac{25 π}{12}

como

2 π + \frac{π}{12}

= csc (2 π + \frac{π}{12})

Utilizar la periodicidad de

csc

csc (x + 2 π) = csc (x)

csc (2 π + \frac{π}{12}) = csc (\frac{π}{12})

= csc (\frac{π}{12})

= (- sin (\frac{π}{12})) csc (\frac{π}{12})

Simplificar

= - sin (\frac{π}{12}) csc (\frac{π}{12})

Re-escribir usando identidades trigonométricas:

sin (\frac{π}{12}) = \frac{1}{csc ( \frac{π}{12} )}

sin (\frac{π}{12})

Utilizar la identidad trigonométrica básica:

sin (x) = \frac{1}{csc ( x )}

= \frac{1}{csc ( \frac{π}{12} )}

= - \frac{1}{csc ( \frac{π}{12} )} csc (\frac{π}{12})

- \frac{1}{csc ( \frac{π}{12} )} csc (\frac{π}{12}) = - 1

- \frac{1}{csc ( \frac{π}{12} )} csc (\frac{π}{12})

Multiplicar fracciones:

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

= - \frac{1 \cdot csc ( \frac{π}{12} )}{csc ( \frac{π}{12} )}

Eliminar los terminos comunes:

csc (\frac{π}{12})

= - 1

= - 1

80 \cdot cos (6 0^{\circ})

arcsin (\frac{16}{34})

1 + tan (\frac{π}{4})

3 sin^{2} (π)

15 sin (4 0^{\circ})