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العربية

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

الحلّ

prove

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

صحيح

خطوات الحلّ

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

قم بالعمل على الطرف الأيسر

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

sin (- x) = - sin (x)

:Use the negative angle identity

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

tan (- x) = - tan (x)

:Use the negative angle identity

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

sec (- x) = sec (x)

:Use the negative angle identity

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

sin, cos :

عبّر بواسطة

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

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

:Use the basic trigonometric identity

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

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

:Use the basic trigonometric identity

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

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

بسّط:

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

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

- (- a) = a

فعّل القانون

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

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

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

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

:اضرب كسور

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

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

sin (x) sin (x)

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

:فعّل قانون القوى

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

= sin^{1 + 1} (x)

1 + 1 = 2 :

اجمع الأعداد

= sin^{2} (x)

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

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

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

فعّل القانون

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

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

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

Rewrite using trig identities

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

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

:فعّل نطريّة فيتاغوروس

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

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

cos (x) :

إلغ العوامل المشتركة

= cos (x)

= cos (x)

أظهرنا بأنّ الطرفين من الممكن أن تكون لهما نفس الصورة

\Rightarrow صحيح

cos (arcsin (\frac{5}{13}))

arcsec (2)

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

- cos (2 π)

arccos (- \frac{1}{2})