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العربية

prove sec(-x)*sin(x)=tan(x)

الحلّ

prove

sec (- x) \cdot sin (x) = tan (x)

صحيح

خطوات الحلّ

sec (- x) sin (x) = tan (x)

قم بالعمل على الطرف الأيسر

sec (- x) sin (x)

sec (- x) = sec (x)

:Use the negative angle identity

= sec (x) sin (x)

Rewrite using trig identities

sec (x) sin (x)

sin, cos :

عبّر بواسطة

sec (x) sin (x)

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

:Use the basic trigonometric identity

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

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

بسّط:

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

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

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

:اضرب كسور

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

1 \cdot sin (x) = sin (x) :

اضرب

= \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)

= tan (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

p ro v e \frac{cot ^{2} ( x ) - 1}{csc ^{2} ( x )} = cos (2 x)

p ro v e csc^{2} (x) - csc^{2} (x) \cdot cos^{2} (x) = 1

p ro v e cos (θ) - sin (θ) sin (2 θ) = cos (θ) cos (2 θ)

p ro v e 1 + (cot (A))^{2} = \cdot (csc (A))^{2}

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