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شائع علم المثلثات >

cos(A-25)+cos(A+25)=cos(25)

الحلّ

cos (A - 2 5^{\circ}) + cos (A + 2 5^{\circ}) = cos (2 5^{\circ})

الحلّ

A = 6 0^{\circ} + 36 0^{\circ} n, A = 30 0^{\circ} + 36 0^{\circ} n

راديان

A = \frac{π}{3} + 2 πn, A = \frac{5 π}{3} + 2 πn

خطوات الحلّ

cos (A - 2 5^{\circ}) + cos (A + 2 5^{\circ}) = cos (2 5^{\circ})

Rewrite using trig identities

cos (A - 2 5^{\circ}) + cos (A + 2 5^{\circ})

cos (s) + cos (t) = 2 cos (\frac{s + t}{2}) cos (\frac{s - t}{2})

Eq u a t i o n 0 :

متطابقة تحويل الجمع لضرب

= 2 cos (\frac{A - 2 5 ^{\circ} + A + 2 5 ^{\circ}}{2}) cos (\frac{A - 2 5 ^{\circ} - ( A + 2 5 ^{\circ} )}{2})

2 cos (\frac{A - 2 5 ^{\circ} + A + 2 5 ^{\circ}}{2}) cos (\frac{A - 2 5 ^{\circ} - ( A + 2 5 ^{\circ} )}{2})

بسّط:

2 cos (2 5^{\circ}) cos (A)

2 cos (\frac{A - 2 5 ^{\circ} + A + 2 5 ^{\circ}}{2}) cos (\frac{A - 2 5 ^{\circ} - ( A + 2 5 ^{\circ} )}{2})

\frac{A - 2 5 ^{\circ} + A + 2 5 ^{\circ}}{2} = A

\frac{A - 2 5 ^{\circ} + A + 2 5 ^{\circ}}{2}

A - 2 5^{\circ} + A + 2 5^{\circ} = 2 A

A - 2 5^{\circ} + A + 2 5^{\circ}

جمّع التعابير المتشابهة

= A + A - 2 5^{\circ} + 2 5^{\circ}

A + A = 2 A :

اجمع العناصر المتشابهة

= 2 A - 2 5^{\circ} + 2 5^{\circ}

- 2 5^{\circ} + 2 5^{\circ} = 0 :

اجمع العناصر المتشابهة

= 2 A

= \frac{2 A}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= A

= 2 cos (A) cos (\frac{A - ( A + 2 5 ^{\circ} ) - 2 5 ^{\circ}}{2})

\frac{A - 2 5 ^{\circ} - ( A + 2 5 ^{\circ} )}{2} = - 2 5^{\circ}

\frac{A - 2 5 ^{\circ} - ( A + 2 5 ^{\circ} )}{2}

A - 2 5^{\circ} - (A + 2 5^{\circ})

وحّد:

- 5 0^{\circ}

A - 2 5^{\circ} - (A + 2 5^{\circ})

A = \frac{A 36}{36}, (A + 2 5^{\circ}) = \frac{( A + 2 5 ^{\circ} ) 36}{36}

:حوّل الأعداد لكسور

= \frac{A \cdot 36}{36} - 2 5^{\circ} - \frac{( A + 2 5 ^{\circ} ) \cdot 36}{36}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{A \cdot 36 - 90 0 ^{\circ} - ( A + 2 5 ^{\circ} ) \cdot 36}{36}

A \cdot 36 - 90 0^{\circ} - (A + 2 5^{\circ}) \cdot 36

وسٌع:

- 180 0^{\circ}

A \cdot 36 - 90 0^{\circ} - (A + 2 5^{\circ}) \cdot 36

= 36 A - 90 0^{\circ} - 36 (A + 2 5^{\circ})

- 36 (A + 2 5^{\circ})

وسٌع:

- 36 A - 90 0^{\circ}

- 36 (A + 2 5^{\circ})

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 36, b = A, c = 2 5^{\circ}

= - 36 A + (- 36) 2 5^{\circ}

فعّل قوانين سالب-موجب

+ (- a) = - a

= - 36 A - 36 \cdot 2 5^{\circ}

36 \cdot 2 5^{\circ} = 90 0^{\circ}

36 \cdot 2 5^{\circ}

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

:اضرب كسور

= 90 0^{\circ}

36 :

إلغ العوامل المشتركة

= 90 0^{\circ}

= - 36 A - 90 0^{\circ}

= A \cdot 36 - 90 0^{\circ} - 36 A - 90 0^{\circ}

A \cdot 36 - 90 0^{\circ} - 36 A - 90 0^{\circ}

بسّط:

- 180 0^{\circ}

A \cdot 36 - 90 0^{\circ} - 36 A - 90 0^{\circ}

جمّع التعابير المتشابهة

= 36 A - 36 A - 90 0^{\circ} - 90 0^{\circ}

36 A - 36 A = 0 :

اجمع العناصر المتشابهة

= - 90 0^{\circ} - 90 0^{\circ}

- 90 0^{\circ} - 90 0^{\circ} = - 180 0^{\circ} :

اجمع العناصر المتشابهة

= - 180 0^{\circ}

= - 180 0^{\circ}

= \frac{- 180 0 ^{\circ}}{36}

\frac{- a}{b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - 5 0^{\circ}

2 :

إلغ العوامل المشتركة

= - 5 0^{\circ}

= \frac{- 5 0 ^{\circ}}{2}

\frac{- a}{b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{5 0 ^{\circ}}{2}

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

: استخدم ميزات الكسور التالية

\frac{5 0 ^{\circ}}{2} = \frac{90 0 ^{\circ}}{18 \cdot 2}

= - \frac{90 0 ^{\circ}}{18 \cdot 2}

18 \cdot 2 = 36 :

اضرب الأعداد

= - 2 5^{\circ}

= 2 cos (- 2 5^{\circ}) cos (A)

cos (- 2 5^{\circ})

بسّط:

cos (2 5^{\circ})

cos (- 2 5^{\circ})

cos (- x) = cos (x) :

استخدم القانون التالي

cos (- 2 5^{\circ}) = cos (2 5^{\circ})

= cos (2 5^{\circ})

= 2 cos (2 5^{\circ}) cos (A)

= 2 cos (2 5^{\circ}) cos (A)

2 cos (2 5^{\circ}) cos (A) = cos (2 5^{\circ})

2 cos (2 5^{\circ})

اقسم الطرفين على

2 cos (2 5^{\circ}) cos (A) = cos (2 5^{\circ})

2 cos (2 5^{\circ})

اقسم الطرفين على

\frac{2 cos ( 2 5 ^{\circ} ) cos ( A )}{2 cos ( 2 5 ^{\circ} )} = \frac{cos ( 2 5 ^{\circ} )}{2 cos ( 2 5 ^{\circ} )}

بسّط

cos (A) = \frac{1}{2}

cos (A) = \frac{1}{2}

cos (A) = \frac{1}{2} :

حلول عامّة لـ

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

A = 6 0^{\circ} + 36 0^{\circ} n, A = 30 0^{\circ} + 36 0^{\circ} n

A = 6 0^{\circ} + 36 0^{\circ} n, A = 30 0^{\circ} + 36 0^{\circ} n

رسم

أمثلة شائعة

tan^2(θ)-tan(θ)=0,θ,0<= θ<2pi

tan^{2} (θ) - tan (θ) = 0, θ, 0 \leq θ < 2 π

cos(4x)-4cos(2x)=5

cos (4 x) - 4 cos (2 x) = 5

sin(x)=sin(x+(-3)pi)

sin (x) = sin (x + (- 3) π)

sin(2x)-2/3 =0

sin (2 x) - \frac{2}{3} = 0

2sin(θ)+cos(2θ)=0

2 sin (θ) + cos (2 θ) = 0