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شائع علم المثلثات >

sec(x)cot(x)= 7/6

الحلّ

sec (x) cot (x) = \frac{7}{6}

الحلّ

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

+1

درجات

x = 58.99728 \dots^{\circ} + 36 0^{\circ} n, x = 121.00271 \dots^{\circ} + 36 0^{\circ} n

خطوات الحلّ

sec (x) cot (x) = \frac{7}{6}

من الطرفين

\frac{7}{6}

اطرح

sec (x) cot (x) - \frac{7}{6} = 0

sec (x) cot (x) - \frac{7}{6}

بسّط:

\frac{6 sec ( x ) cot ( x ) - 7}{6}

sec (x) cot (x) - \frac{7}{6}

sec (x) cot (x) = \frac{sec ( x ) cot ( x ) 6}{6}

:حوّل الأعداد لكسور

= \frac{sec ( x ) cot ( x ) \cdot 6}{6} - \frac{7}{6}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{sec ( x ) cot ( x ) \cdot 6 - 7}{6}

\frac{6 sec ( x ) cot ( x ) - 7}{6} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

6 sec (x) cot (x) - 7 = 0

sin, cos :

عبّر بواسطة

- 7 + 6 cot (x) sec (x)

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} sec (x)

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

= - 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

بسّط:

\frac{- 7 sin ( x ) + 6}{sin ( x )}

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} = \frac{6}{sin ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

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

:اضرب كسور

= \frac{cos ( x ) \cdot 1 \cdot 6}{sin ( x ) cos ( x )}

cos (x) :

إلغ العوامل المشتركة

= \frac{1 \cdot 6}{sin ( x )}

1 \cdot 6 = 6 :

اضرب الأعداد

= \frac{6}{sin ( x )}

= - 7 + \frac{6}{sin ( x )}

7 = \frac{7 sin ( x )}{sin ( x )}

:حوّل الأعداد لكسور

= - \frac{7 sin ( x )}{sin ( x )} + \frac{6}{sin ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- 7 sin ( x ) + 6}{sin ( x )}

= \frac{- 7 sin ( x ) + 6}{sin ( x )}

\frac{6 - 7 sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

6 - 7 sin (x) = 0

انقل

6

إلى الجانب الأيمن

6 - 7 sin (x) = 0

من الطرفين

6

اطرح

6 - 7 sin (x) - 6 = 0 - 6

بسّط

- 7 sin (x) = - 6

- 7 sin (x) = - 6

- 7

اقسم الطرفين على

- 7 sin (x) = - 6

- 7

اقسم الطرفين على

\frac{- 7 sin ( x )}{- 7} = \frac{- 6}{- 7}

بسّط

sin (x) = \frac{6}{7}

sin (x) = \frac{6}{7}

Apply trig inverse properties

sin (x) = \frac{6}{7}

sin (x) = \frac{6}{7} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

أظهر الحلّ بالتمثيل العشريّ

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

رسم

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