ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sin(x)cos(x)csc^2(x)=cot(x)

الحلّ

prove

sin (x) cos (x) csc^{2} (x) = cot (x)

الحلّ

صحيح

خطوات الحلّ

sin (x) cos (x) csc^{2} (x) = cot (x)

قم بالعمل على الطرف الأيسر

sin (x) cos (x) csc^{2} (x)

sin, cos :

عبّر بواسطة

cos (x) csc^{2} (x) sin (x)

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

:Use the basic trigonometric identity

= cos (x) (\frac{1}{sin ( x )})^{2} sin (x)

cos (x) (\frac{1}{sin ( x )})^{2} sin (x)

بسّط:

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

cos (x) (\frac{1}{sin ( x )})^{2} sin (x)

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

(\frac{1}{sin ( x )})^{2}

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

:فعّل قانون القوى

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

1^{a} = 1

فعّل القانون

1^{2} = 1

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

= \frac{1}{sin ^{2} ( x )} cos (x) sin (x)

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

:اضرب كسور

= \frac{1 \cdot cos ( x ) sin ( x )}{sin ^{2} ( x )}

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

اضرب

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

sin (x) :

إلغ العوامل المشتركة

= \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)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

أمثلة شائعة

prove 4cos^2(x)-2=0 prove

4 cos^{2} (x) - 2 = 0

prove cos(2t)=cos^2(t)-sin^2(t)prove

cos (2 t) = cos^{2} (t) - sin^{2} (t)

prove 2-2tan(x)cot(2x)=sec^2(x)prove

2 - 2 tan (x) cot (2 x) = sec^{2} (x)

prove sec^2(B)-csc^2(B)=(tan(B)-cot(B))/(sin(B)cos(B))prove

sec^{2} (B) - csc^{2} (B) = \frac{tan ( B ) - cot ( B )}{sin ( B ) cos ( B )}

prove 2+sec(a)cos(a)=3 prove

2 + sec (a) cos (a) = 3