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tan(35)tan(56-x)=1

الحلّ

tan (3 5^{\circ}) tan (5 6^{\circ} - x) = 1

الحلّ

x = - 18 0^{\circ} n + 5 6^{\circ} - 0.95993 \dots

راديان

x = \frac{14 π}{45} - 0.95993 \dots - πn

خطوات الحلّ

tan (3 5^{\circ}) tan (5 6^{\circ} - x) = 1

tan (3 5^{\circ})

اقسم الطرفين على

tan (3 5^{\circ}) tan (5 6^{\circ} - x) = 1

tan (3 5^{\circ})

اقسم الطرفين على

\frac{tan ( 3 5 ^{\circ} ) tan ( 5 6 ^{\circ} - x )}{tan ( 3 5 ^{\circ} )} = \frac{1}{tan ( 3 5 ^{\circ} )}

بسّط

tan (5 6^{\circ} - x) = \frac{1}{tan ( 3 5 ^{\circ} )}

tan (5 6^{\circ} - x) = \frac{1}{tan ( 3 5 ^{\circ} )}

Apply trig inverse properties

tan (5 6^{\circ} - x) = \frac{1}{tan ( 3 5 ^{\circ} )}

tan (5 6^{\circ} - x) = \frac{1}{tan ( 3 5 ^{\circ} )} :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

5 6^{\circ} - x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n

5 6^{\circ} - x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n

5 6^{\circ} - x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n

حلّ:

x = - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

5 6^{\circ} - x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n

انقل

5 6^{\circ}

إلى الجانب الأيمن

5 6^{\circ} - x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n

من الطرفين

5 6^{\circ}

اطرح

5 6^{\circ} - x - 5 6^{\circ} = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n - 5 6^{\circ}

بسّط

- x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n - 5 6^{\circ}

- x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n - 5 6^{\circ}

- 1

اقسم الطرفين على

- x = arctan (\frac{1}{tan ( 3 5 ^{\circ} )}) + 18 0^{\circ} n - 5 6^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{5 6 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{5 6 ^{\circ}}{- 1}

\frac{- x}{- 1}

بسّط:

x

\frac{- x}{- 1}

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

: استخدم ميزات الكسور التالية

= \frac{x}{1}

\frac{a}{1} = a

فعّل القانون

= x

\frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{5 6 ^{\circ}}{- 1}

بسّط:

- 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

\frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{5 6 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{18 0 ^{\circ} n}{- 1} - \frac{5 6 ^{\circ}}{- 1} + \frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1}

\frac{18 0 ^{\circ} n}{- 1} = - 18 0^{\circ} n

\frac{18 0 ^{\circ} n}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{18 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 18 0^{\circ} n

= - 18 0^{\circ} n - \frac{5 6 ^{\circ}}{- 1} + \frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1}

\frac{5 6 ^{\circ}}{- 1} = - 5 6^{\circ}

\frac{5 6 ^{\circ}}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{5 6 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{5 6 ^{\circ}}{1} = 5 6^{\circ}

= - 5 6^{\circ}

\frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1} = - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

\frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{arctan ( \frac{1}{t a n ( 3 5 ^{\circ} )} )}{1} = arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

= - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

= - 18 0^{\circ} n - (- 5 6^{\circ}) - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

- (- a) = a

فعّل القانون

= - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

x = - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

x = - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

x = - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

x = - 18 0^{\circ} n + 5 6^{\circ} - arctan (\frac{1}{tan ( 3 5 ^{\circ} )})

أظهر الحلّ بالتمثيل العشريّ

x = - 18 0^{\circ} n + 5 6^{\circ} - 0.95993 \dots

أمثلة شائعة

42.25=0.1681cos(b)

42.25 = 0.1681 cos (b)

(tan(3x))/(tan(2x))=1

\frac{tan ( 3 x )}{tan ( 2 x )} = 1

6cot(x)=5-tan(x)

6 cot (x) = 5 - tan (x)

3cos(θ)-3=0

3 cos (θ) - 3 = 0

(sqrt(3)tan(x)-1)(tan(x)-sqrt(3))=0

(3 tan (x) - 1) (tan (x) - 3) = 0