English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove csc(x)-cos(x)*cot(x)=sin(x)

الحلّ

prove

csc (x) - cos (x) \cdot cot (x) = sin (x)

صحيح

خطوات الحلّ

csc (x) - cos (x) cot (x) = sin (x)

قم بالعمل على الطرف الأيسر

csc (x) - cos (x) cot (x)

sin, cos :

عبّر بواسطة

csc (x) - cos (x) cot (x)

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

:Use the basic trigonometric identity

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

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

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

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

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

:اضرب كسور

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

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

a^{b} \cdot a^{c} = a^{b + c}

:فعّل قانون القوى

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

1 + 1 = 2 :

اجمع الأعداد

= cos^{2} (x)

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

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

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

فعّل القانون

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

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

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

Rewrite using trig identities

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

1 = cos^{2} (x) + sin^{2} (x)

:فعّل نطريّة فيتاغوروس

1 - cos^{2} (x) = sin^{2} (x)

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

sin (x) :

إلغ العوامل المشتركة

= sin (x)

= sin (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e sin (x) \cdot csc (x) = 1

p ro v e csc^{2} (θ) (1 - cos^{2} (θ)) = sin (648 0^{\circ})

p ro v e sin (2 x) = \frac{( 2 tan ( x ) )}{1 + tan ^{2} ( x )}

p ro v e \frac{1 + sec ( θ )}{sec ( θ )} = 2 cos^{2} (\frac{θ}{2})

p ro v e \frac{1 - 2 sin ^{2} ( x )}{sin ( x ) cos ( x )} = cot (x) - tan (x)