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شائع علم المثلثات >

3cos^2(x)-cos(2x)=1

الحلّ

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

الحلّ

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

درجات

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

خطوات الحلّ

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

من الطرفين

1

اطرح

3 cos^{2} (x) - cos (2 x) - 1 = 0

Rewrite using trig identities

- 1 - cos (2 x) + 3 cos^{2} (x)

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

:فعّل متطابقة الزاوية المضاعفة

= - 1 - (2 cos^{2} (x) - 1) + 3 cos^{2} (x)

- 1 - (2 cos^{2} (x) - 1) + 3 cos^{2} (x)

بسّط:

cos^{2} (x)

- 1 - (2 cos^{2} (x) - 1) + 3 cos^{2} (x)

- (2 cos^{2} (x) - 1) : - 2 cos^{2} (x) + 1

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

افتح أقواس

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

فعّل قوانين سالب-موجب

- (- a) = a, - (a) = - a

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

= - 1 - 2 cos^{2} (x) + 1 + 3 cos^{2} (x)

- 1 - 2 cos^{2} (x) + 1 + 3 cos^{2} (x)

بسّط:

cos^{2} (x)

- 1 - 2 cos^{2} (x) + 1 + 3 cos^{2} (x)

جمّع التعابير المتشابهة

= - 2 cos^{2} (x) + 3 cos^{2} (x) - 1 + 1

- 2 cos^{2} (x) + 3 cos^{2} (x) = cos^{2} (x) :

اجمع العناصر المتشابهة

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

- 1 + 1 = 0

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

cos^{2} (x) = 0

x^{n} = 0 \Rightarrow x = 0

فعّل القانون

cos (x) = 0

cos (x) = 0 :

حلول عامّة لـ

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

رسم

أمثلة شائعة

sin(2x)+sin(4x)=cos(x)

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2 sin (x) = - 0.684

tan(x-60)=-1.26

tan (x - 6 0^{\circ}) = - 1.26

3 sec (x) = - 5

tan(3x-10)=cot(2x-40)

tan (3 x - 10) = cot (2 x - 40)