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شائع >

csc(A)*tan(A)=sin(A)

الحلّ

csc (A) \cdot tan (A) = sin (A)

الحلّ

A \in R لا يوجد حلّ لـ

خطوات الحلّ

csc (A) tan (A) = sin (A)

من الطرفين

sin (A)

اطرح

csc (A) tan (A) - sin (A) = 0

sin, cos :

عبّر بواسطة

- sin (A) + csc (A) tan (A)

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

:Use the basic trigonometric identity

= - sin (A) + \frac{1}{sin ( A )} tan (A)

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

:Use the basic trigonometric identity

= - sin (A) + \frac{1}{sin ( A )} \cdot \frac{sin ( A )}{cos ( A )}

- sin (A) + \frac{1}{sin ( A )} \cdot \frac{sin ( A )}{cos ( A )}

بسّط:

\frac{- sin ( A ) cos ( A ) + 1}{cos ( A )}

- sin (A) + \frac{1}{sin ( A )} \cdot \frac{sin ( A )}{cos ( A )}

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

\frac{1}{sin ( A )} \cdot \frac{sin ( A )}{cos ( A )}

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

:اضرب كسور

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

sin (A) :

إلغ العوامل المشتركة

= \frac{1}{cos ( A )}

= - sin (A) + \frac{1}{cos ( A )}

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

:حوّل الأعداد لكسور

= - \frac{sin ( A ) cos ( A )}{cos ( A )} + \frac{1}{cos ( A )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- sin ( A ) cos ( A ) + 1}{cos ( A )}

= \frac{- sin ( A ) cos ( A ) + 1}{cos ( A )}

\frac{1 - cos ( A ) sin ( A )}{cos ( A )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - cos (A) sin (A) = 0

Rewrite using trig identities

1 - cos (A) sin (A)

2 sin (x) cos (x) = sin (2 x)

:فعّل متطابقة الزاوية المضاعفة

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

= 1 - \frac{sin ( 2 A )}{2}

1 - \frac{sin ( 2 A )}{2} = 0

انقل

1

إلى الجانب الأيمن

1 - \frac{sin ( 2 A )}{2} = 0

من الطرفين

1

اطرح

1 - \frac{sin ( 2 A )}{2} - 1 = 0 - 1

بسّط

- \frac{sin ( 2 A )}{2} = - 1

- \frac{sin ( 2 A )}{2} = - 1

2

اضرب الطرفين بـ

- \frac{sin ( 2 A )}{2} = - 1

2

اضرب الطرفين بـ

2 (- \frac{sin ( 2 A )}{2}) = 2 (- 1)

بسّط

- sin (2 A) = - 2

- sin (2 A) = - 2

- 1

اقسم الطرفين على

- sin (2 A) = - 2

- 1

اقسم الطرفين على

\frac{- sin ( 2 A )}{- 1} = \frac{- 2}{- 1}

بسّط

sin (2 A) = 2

sin (2 A) = 2

- 1 \leq sin (x) \leq 1

A \in R لا يوجد حلّ لـ

أمثلة شائعة

cos(x)=sqrt(2/3)

cos (x) = \frac{2}{3}

(sec(3x)-sqrt(2))(tan(2x)-1)=0

(sec (3 x) - 2) (tan (2 x) - 1) = 0

cos(2x)*2-2cos(x)=0

cos (2 x) \cdot 2 - 2 cos (x) = 0

-2sin(2x)= pi/(12)

- 2 sin (2 x) = \frac{π}{12}

cos(x)=(sec(x))/4

cos (x) = \frac{sec ( x )}{4}