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شائع علم المثلثات >

cot(38)=tan(2x)

الحلّ

cot (3 8^{\circ}) = tan (2 x)

الحلّ

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

+1

راديان

x = \frac{13 π}{90} + \frac{π}{2} n

خطوات الحلّ

cot (3 8^{\circ}) = tan (2 x)

بدّل الأطراف

tan (2 x) = cot (3 8^{\circ})

Apply trig inverse properties

tan (2 x) = cot (3 8^{\circ})

tan (2 x) = cot (3 8^{\circ}) :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

2 x = arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

2 x = arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

2 x = arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

حلّ:

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

2 x = arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

بسّط:

5 2^{\circ} + 18 0^{\circ} n

arctan (cot (3 8^{\circ})) + 18 0^{\circ} n

arctan (cot (3 8^{\circ})) = 5 2^{\circ}

arctan (cot (3 8^{\circ}))

Rewrite using trig identities:

cot (3 8^{\circ}) = tan (5 2^{\circ})

cot (3 8^{\circ})

tan (9 0^{\circ} - x) = cot (x)

= tan (9 0^{\circ} - 3 8^{\circ})

= tan (5 2^{\circ})

= arctan (tan (5 2^{\circ}))

Use the inverse trig property:

5 2^{\circ}

arctan (tan (5 2^{\circ}))

a rc t an (t an (x)) = x, - 9 0^{\circ} < x < 9 0^{\circ}

من أجل

- 9 0^{\circ} < 5 2^{\circ} < 9 0^{\circ}

= 5 2^{\circ}

= 5 2^{\circ}

= 5 2^{\circ} + 18 0^{\circ} n

2 x = 5 2^{\circ} + 18 0^{\circ} n

2

اقسم الطرفين على

2 x = 5 2^{\circ} + 18 0^{\circ} n

2

اقسم الطرفين على

\frac{2 x}{2} = \frac{5 2 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

بسّط

\frac{2 x}{2} = \frac{5 2 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

\frac{5 2 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

بسّط:

2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

\frac{5 2 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

\frac{5 2 ^{\circ}}{2} = 2 6^{\circ}

\frac{5 2 ^{\circ}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{234 0 ^{\circ}}{45 \cdot 2}

45 \cdot 2 = 90 :

اضرب الأعداد

= 2 6^{\circ}

= 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

x = 2 6^{\circ} + \frac{18 0 ^{\circ} n}{2}

رسم

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