prove (1-sin^2(x))*csc^2(x)=cot^2(x)

الحلّ

prove

(1 - sin^{2} (x)) \cdot csc^{2} (x) = cot^{2} (x)

صحيح

خطوات الحلّ

(1 - sin^{2} (x)) csc^{2} (x) = cot^{2} (x)

قم بالعمل على الطرف الأيمن

cot^{2} (x)

sin, cos :

عبّر بواسطة

cot^{2} (x)

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

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

:فعّل قانون القوى

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

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

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

Rewrite using trig identities

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

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

:فعّل نطريّة فيتاغوروس

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

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

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

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

:Use the basic trigonometric identity

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

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e cot^{2} (θ) - cos^{2} (θ) = cot^{2} (θ) cos^{2} (θ)

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

p ro v e sin (x) cos (x) + sin^{3} (x) sec (x) = tan (x)

p ro v e - tan (θ) cos (θ) = sin (- θ)

p ro v e sec (t) - \frac{cos ( t )}{1 + sin ( t )} = tan (t)