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עברית

العربية

(tan(x)+cot(x))/(csc(x))=cos(x)

الحلّ

\frac{tan ( x ) + cot ( x )}{csc ( x )} = cos (x)

x \in R لا يوجد حلّ لـ

خطوات الحلّ

\frac{tan ( x ) + cot ( x )}{csc ( x )} = cos (x)

من الطرفين

cos (x)

اطرح

\frac{tan ( x ) + cot ( x )}{csc ( x )} - cos (x) = 0

\frac{tan ( x ) + cot ( x )}{csc ( x )} - cos (x)

بسّط:

\frac{tan ( x ) + cot ( x ) - cos ( x ) csc ( x )}{csc ( x )}

\frac{tan ( x ) + cot ( x )}{csc ( x )} - cos (x)

cos (x) = \frac{cos ( x ) csc ( x )}{csc ( x )}

:حوّل الأعداد لكسور

= \frac{tan ( x ) + cot ( x )}{csc ( x )} - \frac{cos ( x ) csc ( x )}{csc ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{tan ( x ) + cot ( x ) - cos ( x ) csc ( x )}{csc ( x )}

\frac{tan ( x ) + cot ( x ) - cos ( x ) csc ( x )}{csc ( x )} = 0

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

tan (x) + cot (x) - cos (x) csc (x) = 0

Rewrite using trig identities

cot (x) + tan (x) - cos (x) csc (x)

csc (x) cos (x) = cot (x)

csc (x) cos (x)

sin, cos :

عبّر بواسطة

csc (x) cos (x)

csc (x) = \frac{1}{sin ( x )}

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

:اضرب كسور

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

1 \cdot cos (x) = cos (x) :

اضرب

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

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

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

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

:Use the basic trigonometric identity

= cot (x)

= cot (x) + tan (x) - cot (x)

بسّط

= tan (x)

tan (x) = 0

tan (x) = 0 :

حلول عامّة لـ

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

x = 0 + πn

حلّ:

x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

πn :

بما أنّ المعادلة غير معرّفة لـ

x \in R لا يوجد حلّ لـ

tan (θ) = - \frac{3}{7}

2 sin (\frac{x}{2}) = 2

cos (θ) = 0.7071

2 cos (x) - 5 sin (x) = 0

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