prove (sec(x))/(csc(x))=tan(x)

الحلّ

prove

\frac{sec ( x )}{csc ( x )} = tan (x)

صحيح

خطوات الحلّ

\frac{sec ( x )}{csc ( x )} = tan (x)

قم بالعمل على الطرف الأيسر

\frac{sec ( x )}{csc ( x )}

sin, cos :

عبّر بواسطة

\frac{sec ( x )}{csc ( x )}

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

:Use the basic trigonometric identity

= \frac{\frac{1}{c o s ( x )}}{csc ( x )}

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

:Use the basic trigonometric identity

= \frac{\frac{1}{c o s ( x )}}{\frac{1}{s i n ( x )}}

\frac{\frac{1}{c o s ( x )}}{\frac{1}{s i n ( x )}}

بسّط:

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

\frac{\frac{1}{c o s ( x )}}{\frac{1}{s i n ( x )}}

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

:اقسم الكسور

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

بسّط

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

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

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

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

:Use the basic trigonometric identity

= tan (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e cot^{2} (θ) (1 + tan^{2} (θ)) = csc^{2} (θ)

p ro v e tan^{2} (u) - sin^{2} (u) = tan^{2} (u) sin^{2} (u)

p ro v e 1 - tan^{4} (A) = 2 sec^{2} (A) - sec^{4} (A)

p ro v e cos^{4} (θ) - sin^{4} (θ) = 2 cos^{2} (θ) - 1

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