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

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيمن

csc (x) cot (x)

sin, cos :

عبّر بواسطة

cot (x) csc (x)

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

:Use the basic trigonometric identity

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

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

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

:اضرب كسور

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

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

اضرب

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

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

sin (x) sin (x)

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

:فعّل قانون القوى

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

= sin^{1 + 1} (x)

1 + 1 = 2 :

اجمع الأعداد

= sin^{2} (x)

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

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

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

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e tan (2 x) - tan (x) = tan (x) sec (2 x)

p ro v e cos (2 a) = 2 cos^{2} (a) - 1

p ro v e 1 + sec (x) = \frac{cos ( x ) + 1}{cos ( x )}

p ro v e sec (2 θ) = \frac{sec ^{2} ( θ ) csc ^{2} ( θ )}{csc ^{2} ( θ ) - sec ^{2} ( θ )}

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