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شائع علم المثلثات >

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

الحلّ

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

الحلّ

1

خطوات الحلّ

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

استخدم المتطابقة الأساسيّة التالية:

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

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

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}

استخدم المتطابقة الأساسيّة التالية:

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

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

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}

استخدم المتطابقة الأساسيّة التالية:

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

tan (6 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

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

استخدم المتطابقة الأساسيّة التالية:

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

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

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}}

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

بسّط:

1

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

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

وحّد الكسور:

1

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

فعّل القانون

= \frac{1 + 1}{2}

1 + 1 = 2 :

اجمع الأعداد

= \frac{2}{2}

\frac{a}{a} = 1

فعّل القانون

= 1

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

3 \frac{3}{3}

اضرب بـ:

1

3 \frac{3}{3}

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

:اضرب كسور

= \frac{3 3}{3}

33 = 3

33

a a = a

:فعْل قانون الجذور

33 = 3

= 3

= \frac{3}{3}

\frac{a}{a} = 1

فعّل القانون

= 1

= \frac{1}{1}

\frac{a}{1} = a

فعّل القانون

= 1

= 1

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