English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove tan(θ)=(sec(θ))/(csc(θ))

الحلّ

prove

tan (θ) = \frac{sec ( θ )}{csc ( θ )}

صحيح

خطوات الحلّ

tan (θ) = \frac{sec ( θ )}{csc ( θ )}

قم بالعمل على الطرف الأيسر

tan (θ)

sin, cos :

عبّر بواسطة

tan (θ)

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

:Use the basic trigonometric identity

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

Rewrite using trig identities

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

:Use the basic trigonometric identity

\frac{\frac{1}{c s c ( θ )}}{cos ( θ )}

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

:Use the basic trigonometric identity

\frac{\frac{1}{c s c ( θ )}}{\frac{1}{s e c ( θ )}}

بسّط

\frac{\frac{1}{c s c ( θ )}}{\frac{1}{s e c ( θ )}}

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

:اقسم الكسور

= \frac{1 \cdot sec ( θ )}{csc ( θ ) \cdot 1}

بسّط

= \frac{sec ( θ )}{csc ( θ )}

\frac{sec ( θ )}{csc ( θ )}

\frac{sec ( θ )}{csc ( θ )}

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e cos (3 β) = cos (β) (cos^{2} (β) - 3 sin^{2} (β))

p ro v e sec^{2} (θ) cot^{2} (θ) - 1 = cot^{2} (θ)

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

p ro v e 2 sin^{2} (3 x) = 1 - cos (6 x)

p ro v e cos (\frac{π}{2} + y) = - sin (y)