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sin(2arcsin(-(sqrt(2))/2))

الحلّ

sin (2 arcsin (- \frac{2}{2}))

الحلّ

- 1

خطوات الحلّ

sin (2 arcsin (- \frac{2}{2}))

Rewrite using trig identities:

- 2 sin (arcsin (\frac{2}{2})) cos (arcsin (\frac{2}{2}))

sin (2 arcsin (- \frac{2}{2}))

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

:فعّل متطابقة الزاوية المضاعفة

= 2 sin (arcsin (- \frac{2}{2})) cos (arcsin (- \frac{2}{2}))

arcsin (- x) = - arcsin (x) :

استخدم القانون التالي

arcsin (- \frac{2}{2}) = - arcsin (\frac{2}{2})

= 2 sin (arcsin (- \frac{2}{2})) cos (- arcsin (\frac{2}{2}))

cos (- x) = cos (x) :

استخدم القانون التالي

cos (- arcsin (\frac{2}{2})) = cos (arcsin (\frac{2}{2}))

= 2 sin (arcsin (- \frac{2}{2})) cos (arcsin (\frac{2}{2}))

arcsin (- x) = - arcsin (x) :

استخدم القانون التالي

arcsin (- \frac{2}{2}) = - arcsin (\frac{2}{2})

= 2 sin (- arcsin (\frac{2}{2})) cos (arcsin (\frac{2}{2}))

sin (- x) = - sin (x) :

استخدم القانون التالي

sin (- arcsin (\frac{2}{2})) = - sin (arcsin (\frac{2}{2}))

= 2 (- sin (arcsin (\frac{2}{2}))) cos (arcsin (\frac{2}{2}))

بسّط

= - 2 sin (arcsin (\frac{2}{2})) cos (arcsin (\frac{2}{2}))

= - 2 sin (arcsin (\frac{2}{2})) cos (arcsin (\frac{2}{2}))

Rewrite using trig identities:

sin (arcsin (\frac{2}{2})) = \frac{2}{2}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{2}{2}

Rewrite using trig identities:

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

cos (arcsin (\frac{2}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{2}{2})) = 1 - (\frac{2}{2})^{2}

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

استخدم المتطابقة التالية

= 1 - (\frac{2}{2})^{2}

= 1 - (\frac{2}{2})^{2}

بسّط

= \frac{1}{2}

= - 2 \cdot \frac{2}{2} \frac{1}{2}

- 2 \cdot \frac{2}{2} \frac{1}{2}

بسّط:

- 1

- 2 \cdot \frac{2}{2} \frac{1}{2}

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

:اضرب كسور

= - \frac{2 \cdot 2 \frac{1}{2}}{2}

2 :

إلغ العوامل المشتركة

= - 2 \frac{1}{2}

a b = a \cdot b

:فعْل قانون الجذور

2 \frac{1}{2} = 2 \cdot \frac{1}{2}

= - 2 \cdot \frac{1}{2}

2 \cdot \frac{1}{2} = 1

2 \cdot \frac{1}{2}

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

:اضرب كسور

= \frac{1 \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= 1

= - 1

1 = 1

فعّل القانون

= - 1

= - 1

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