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شائع علم المثلثات >

(cos(60)+cos(30))/(csc^2(30)+sin^2(45))

الحلّ

\frac{cos ( 6 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{csc ^{2} ( 3 0 ^{\circ} ) + sin ^{2} ( 4 5 ^{\circ} )}

الحلّ

\frac{1 + 3}{9}

عشري

0.30356 \dots

خطوات الحلّ

\frac{cos ( 6 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}{csc ^{2} ( 3 0 ^{\circ} ) + sin ^{2} ( 4 5 ^{\circ} )}

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:

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

cos (3 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{3}{2}

استخدم المتطابقة الأساسيّة التالية:

csc (3 0^{\circ}) = 2

csc (3 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

استخدم المتطابقة الأساسيّة التالية:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{\frac{1}{2} + \frac{3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}}

\frac{\frac{1}{2} + \frac{3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}}

بسّط:

\frac{1 + 3}{9}

\frac{\frac{1}{2} + \frac{3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}}

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

وحّد الكسور:

\frac{1 + 3}{2}

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

فعّل القانون

= \frac{1 + 3}{2}

= \frac{\frac{1 + 3}{2}}{2 ^{2} + ( \frac{2}{2} ) ^{2}}

2^{2} = 4

= \frac{\frac{1 + 3}{2}}{4 + ( \frac{2}{2} ) ^{2}}

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

: استخدم ميزات الكسور التالية

= \frac{1 + 3}{2 ( 4 + ( \frac{2}{2} ) ^{2} )}

(\frac{2}{2})^{2} = \frac{1}{2}

(\frac{2}{2})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:فعّل قانون القوى

= \frac{( 2 ) ^{2}}{2 ^{2}}

(2)^{2} : 2

a = a^{\frac{1}{2}}

:فعْل قانون الجذور

= (2^{\frac{1}{2}})^{2}

(a^{b})^{c} = a^{b c}

:فعّل قانون القوى

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

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

:اضرب كسور

= \frac{1 \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 1

= 2

= \frac{2}{2 ^{2}}

2 :

إلغ العوامل المشتركة

= \frac{1}{2}

= \frac{1 + 3}{2 ( \frac{1}{2} + 4 )}

4 + \frac{1}{2}

وحّد:

\frac{9}{2}

4 + \frac{1}{2}

4 = \frac{4 \cdot 2}{2}

:حوّل الأعداد لكسور

= \frac{4 \cdot 2}{2} + \frac{1}{2}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{4 \cdot 2 + 1}{2}

4 \cdot 2 + 1 = 9

4 \cdot 2 + 1

4 \cdot 2 = 8 :

اضرب الأعداد

= 8 + 1

8 + 1 = 9 :

اجمع الأعداد

= 9

= \frac{9}{2}

= \frac{1 + 3}{2 \cdot \frac{9}{2}}

2 \cdot \frac{9}{2}

اضرب بـ:

9

2 \cdot \frac{9}{2}

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

:اضرب كسور

= \frac{9 \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 9

= \frac{1 + 3}{9}

= \frac{1 + 3}{9}

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tan^2(60)-3cot^2(60)

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5.9tan(59)

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-(cos(-2+2))/2

- \frac{cos ( - 2 + 2 )}{2}

-0*cos(pi/4)-sin(0)

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