English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove (sin^2(-x))/(tan^2(x))=cos^2(x)

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيسر

\frac{sin ^{2} ( - x )}{tan ^{2} ( x )}

sin (- x) = - sin (x)

:Use the negative angle identity

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

sin, cos :

عبّر بواسطة

\frac{( - sin ( x ) ) ^{2}}{tan ^{2} ( x )}

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

:Use the basic trigonometric identity

= \frac{( - sin ( x ) ) ^{2}}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

\frac{( - sin ( x ) ) ^{2}}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

بسّط:

cos^{2} (x)

\frac{( - sin ( x ) ) ^{2}}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

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

(- sin (x))^{2}

زوجيّ n

إذا تحقّق أنّ

, (- a)^{n} = a^{n}

:فعّل قانون القوى

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

= sin^{2} (x)

= \frac{sin ^{2} ( x )}{( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

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

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

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

:فعّل قانون القوى

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

= \frac{sin ^{2} ( x )}{\frac{s i n ^{2} ( x )}{c o s ^{2} ( x )}}

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

: استخدم ميزات الكسور التالية

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

sin^{2} (x) :

إلغ العوامل المشتركة

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

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)

p ro v e sin^{2} (x) csc^{2} (x) - sin^{2} (x) = cos^{2} (x)

p ro v e (sec (u) - tan (u)) (csc (u) + 1) = cot (u)