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עברית

العربية

prove (1+tan^2(x))(sin^2(x))=tan^2(x)

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيسر

(1 + tan^{2} (x)) sin^{2} (x)

Rewrite using trig identities

(1 + tan^{2} (x)) sin^{2} (x)

tan^{2} (x) + 1 = sec^{2} (x)

:فعّل نطريّة فيتاغوروس

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

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

sin, cos :

عبّر بواسطة

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

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

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

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

:فعّل قانون القوى

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

1^{a} = 1

فعّل القانون

1^{2} = 1

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

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

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

:اضرب كسور

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

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

اضرب

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

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

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

Rewrite using trig identities

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

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

:Use the basic trigonometric identity

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

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

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

:Use the basic trigonometric identity

tan (x) tan (x)

tan (x) tan (x)

بسّط:

tan^{2} (x)

tan (x) tan (x)

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

:فعّل قانون القوى

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

= tan^{1 + 1} (x)

1 + 1 = 2 :

اجمع الأعداد

= tan^{2} (x)

tan^{2} (x)

tan^{2} (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e tan (\frac{11}{12} π) = tan (- \frac{π}{12})

p ro v e cot (B) sec (B) sin (B) = 1

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

p ro v e \frac{1 + cot ( x )}{csc ( x )} = sin (x) cos (x)

p ro v e sin^{2} (θ - α) = cos (θ)