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sin(arccos(8/10)+arctan(-6/8))

الحلّ

sin (arccos (\frac{8}{10}) + arctan (- \frac{6}{8}))

الحلّ

0

خطوات الحلّ

sin (arccos (\frac{8}{10}) + arctan (- \frac{6}{8}))

بسّط:

arccos (\frac{8}{10}) + arctan (- \frac{6}{8}) = arccos (\frac{4}{5}) + arctan (- \frac{3}{4})

arccos (\frac{8}{10}) + arctan (- \frac{6}{8})

\frac{8}{10} = \frac{4}{5}

\frac{8}{10}

2 :

إلغ العوامل المشتركة

= \frac{4}{5}

= arccos (\frac{4}{5}) + arctan (- \frac{6}{8})

\frac{6}{8} = \frac{3}{4}

\frac{6}{8}

2 :

إلغ العوامل المشتركة

= \frac{3}{4}

= arccos (\frac{4}{5}) + arctan (- \frac{3}{4})

= sin (arccos (\frac{4}{5}) + arctan (- \frac{3}{4}))

arctan (- x) = - arctan (x) :

استخدم القانون التالي

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

= sin (arccos (\frac{4}{5}) - arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) cos (arctan (\frac{3}{4})) - cos (arccos (\frac{4}{5})) sin (arctan (\frac{3}{4}))

sin (arccos (\frac{4}{5}) - arctan (\frac{3}{4}))

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

:فعّل متطابقة الطرح لزوايا

= sin (arccos (\frac{4}{5})) cos (arctan (\frac{3}{4})) - cos (arccos (\frac{4}{5})) sin (arctan (\frac{3}{4}))

= sin (arccos (\frac{4}{5})) cos (arctan (\frac{3}{4})) - cos (arccos (\frac{4}{5})) sin (arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) = \frac{3}{5}

sin (arccos (\frac{4}{5}))

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) = 1 - (\frac{4}{5})^{2}

sin (arccos (x)) = 1 - x^{2} :

استخدم المتطابقة التالية

= 1 - (\frac{4}{5})^{2}

= 1 - (\frac{4}{5})^{2}

بسّط

= \frac{3}{5}

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) = \frac{4}{5}

cos (arctan (\frac{3}{4}))

Rewrite using trig identities:

cos (arctan (\frac{3}{4})) = \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}} :

استخدم المتطابقة التالية

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

بسّط

= \frac{4}{5}

Rewrite using trig identities:

cos (arccos (\frac{4}{5})) = \frac{4}{5}

cos (arccos (x)) = x :

استخدم المتطابقة التالية

= \frac{4}{5}

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{3}{5}

sin (arctan (\frac{3}{4}))

Rewrite using trig identities:

sin (arctan (\frac{3}{4})) = \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}} :

استخدم المتطابقة التالية

= \frac{( \frac{3}{4} ) 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

= \frac{\frac{3}{4} 1 + ( \frac{3}{4} ) ^{2}}{1 + ( \frac{3}{4} ) ^{2}}

بسّط

= \frac{3}{5}

= \frac{3}{5} \cdot \frac{4}{5} - \frac{4}{5} \cdot \frac{3}{5}

بسّط

= 0

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