حساب المثلثات الأمثلة

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

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

خطوة 1

بسّط القاسم.

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خطوة 1.1

أعِد كتابة

1

$1$ بالصيغة

1^{2}

$1^{2}$ .

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

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

خطوة 1.2

بما أن كلا الحدّين هما مربعان كاملان، حلّل إلى عوامل باستخدام قاعدة الفرق بين مربعين،

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ حيث

a = 1

$a = 1$ و

b = \sin (x)

$b = \sin (x)$ .

\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$

\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$

خطوة 2

اضرب

\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$ في

\frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$ .

\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}} \cdot \frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}} \cdot \frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$

خطوة 3

جمّع وبسّط القاسم.

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خطوة 3.1

اضرب

\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x)}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$ في

\frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}$ .

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))} \sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{\sqrt{(1 + \sin (x)) (1 - \sin (x))} \sqrt{(1 + \sin (x)) (1 - \sin (x))}}$

خطوة 3.2

ارفع

\sqrt{(1 + \sin (x)) (1 - \sin (x))}

$\sqrt{(1 + \sin (x)) (1 - \sin (x))}$ إلى القوة

1

$1$ .

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1} \sqrt{(1 + \sin (x)) (1 - \sin (x))}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1} \sqrt{(1 + \sin (x)) (1 - \sin (x))}}$

خطوة 3.3

ارفع

\sqrt{(1 + \sin (x)) (1 - \sin (x))}

$\sqrt{(1 + \sin (x)) (1 - \sin (x))}$ إلى القوة

1

$1$ .

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1} {\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1} {\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1}}$

خطوة 3.4

استخدِم قاعدة القوة

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1 + 1}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{1 + 1}}$

خطوة 3.5

أضف

1

$1$ و

1

$1$ .

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

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{2}}$

خطوة 3.6

أعِد كتابة

{\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{2}

${\sqrt{(1 + \sin (x)) (1 - \sin (x))}}^{2}$ بالصيغة

(1 + \sin (x)) (1 - \sin (x))

$(1 + \sin (x)) (1 - \sin (x))$ .

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خطوة 3.6.1

استخدِم

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة

\sqrt{(1 + \sin (x)) (1 - \sin (x))}

$\sqrt{(1 + \sin (x)) (1 - \sin (x))}$ في صورة

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

${((1 + \sin (x)) (1 - \sin (x)))}^{\frac{1}{2}}$ .

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

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{({((1 + \sin (x)) (1 - \sin (x)))}^{\frac{1}{2}})}^{2}}$

خطوة 3.6.2

طبّق قاعدة القوة واضرب الأُسس،

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{\frac{1}{2} \cdot 2}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{\frac{1}{2} \cdot 2}}$

خطوة 3.6.3

اجمع

\frac{1}{2}

$\frac{1}{2}$ و

2

$2$ .

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

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{\frac{2}{2}}}$

خطوة 3.6.4

ألغِ العامل المشترك لـ

2

$2$ .

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خطوة 3.6.4.1

ألغِ العامل المشترك.

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

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{\frac{2}{2}}}$

خطوة 3.6.4.2

أعِد كتابة العبارة.

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{1}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{1}}$

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{1}}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{{((1 + \sin (x)) (1 - \sin (x)))}^{1}}$

خطوة 3.6.5

بسّط.

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}$

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}$

\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}

$\frac{\sin (x) \sqrt{(1 + \sin (x)) (1 - \sin (x))}}{(1 + \sin (x)) (1 - \sin (x))}$