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العربية

prove (cos(-x)tan(-x))/(sin(x))=-1

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيسر

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

cos (- x) = cos (x)

:Use the negative angle identity

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

tan (- x) = - tan (x)

:Use the negative angle identity

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

sin, cos :

عبّر بواسطة

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

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

:Use the basic trigonometric identity

= \frac{( - \frac{s i n ( x )}{c o s ( x )} ) cos ( x )}{sin ( x )}

\frac{( - \frac{s i n ( x )}{c o s ( x )} ) cos ( x )}{sin ( x )} = - 1

\frac{( - \frac{s i n ( x )}{c o s ( x )} ) cos ( x )}{sin ( x )}

(- a) = - a

:احذف الأقواس

= \frac{- \frac{s i n ( x )}{c o s ( x )} cos ( x )}{sin ( x )}

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

: استخدم ميزات الكسور التالية

= - \frac{\frac{s i n ( x )}{c o s ( x )} cos ( x )}{sin ( x )}

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

اضرب بـ:

sin (x)

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

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

:اضرب كسور

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

cos (x) :

إلغ العوامل المشتركة

= sin (x)

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

\frac{a}{a} = 1

فعّل القانون

= - 1

= - 1

= - 1

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

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