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(sin(30)+cos(60))/(tan(60)*tan(30))

Solução

\frac{sin ( 3 0 ^{\circ} ) + cos ( 6 0 ^{\circ} )}{tan ( 6 0 ^{\circ} ) \cdot tan ( 3 0 ^{\circ} )}

1

Passos da solução

\frac{sin ( 3 0 ^{\circ} ) + cos ( 6 0 ^{\circ} )}{tan ( 6 0 ^{\circ} ) tan ( 3 0 ^{\circ} )}

Utilizar a seguinte identidade trivial:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

Utilizar a seguinte identidade trivial:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

Utilizar a seguinte identidade trivial:

tan (6 0^{\circ}) = 3

tan (6 0^{\circ})

tan (x)

tabela de periodicidade com ciclo de

18 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

Utilizar a seguinte identidade trivial:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

tabela de periodicidade com ciclo de

18 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{\frac{1}{2} + \frac{1}{2}}{3 \frac{3}{3}}

Simplificar

\frac{\frac{1}{2} + \frac{1}{2}}{3 \frac{3}{3}} : 1

\frac{\frac{1}{2} + \frac{1}{2}}{3 \frac{3}{3}}

Combinar as frações usando o mínimo múltiplo comum:

1

Aplicar a regra

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

= \frac{1 + 1}{2}

Somar:

1 + 1 = 2

= \frac{2}{2}

Aplicar a regra

\frac{a}{a} = 1

= 1

= \frac{1}{3 \frac{3}{3}}

Multiplicar

3 \frac{3}{3} : 1

3 \frac{3}{3}

Multiplicar frações:

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

= \frac{3 3}{3}

33 = 3

33

Aplicar as propriedades dos radicais:

a a = a

33 = 3

= 3

= \frac{3}{3}

Aplicar a regra

\frac{a}{a} = 1

= 1

= \frac{1}{1}

Aplicar a regra

\frac{a}{1} = a

= 1

= 1

cos (\frac{π}{1.5})

sin (- \frac{23 π}{12})

arctan (\frac{900}{480})

arcsin (\frac{10}{10})

- 2 sin (- \frac{π}{4}) - 1