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شائع علم المثلثات >

cos(arctan(4/3)-arcsin(3/5))

الحلّ

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

الحلّ

\frac{24}{25}

+1

عشري

0.96

خطوات الحلّ

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

Rewrite using trig identities:

cos (arctan (\frac{4}{3})) cos (arcsin (\frac{3}{5})) + sin (arctan (\frac{4}{3})) sin (arcsin (\frac{3}{5}))

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

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

:فعّل متطابقة الطرح لزوايا

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

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{3}{5}

Rewrite using trig identities:

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

cos (arcsin (\frac{3}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = 1 - (\frac{3}{5})^{2}

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

استخدم المتطابقة التالية

= 1 - (\frac{3}{5})^{2}

= 1 - (\frac{3}{5})^{2}

بسّط

= \frac{4}{5}

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

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

استخدم المتطابقة التالية

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

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

بسّط

= \frac{4}{5}

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

sin (arcsin (x)) = x :

استخدم المتطابقة التالية

= \frac{3}{5}

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

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5}

بسّط:

\frac{24}{25}

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5}

\frac{3}{5} \cdot \frac{4}{5} + \frac{4}{5} \cdot \frac{3}{5} = 2 \cdot \frac{3}{5} \cdot \frac{4}{5} :

اجمع العناصر المتشابهة

= 2 \cdot \frac{3}{5} \cdot \frac{4}{5}

2 = \frac{2}{1}

:حوّل الأعداد لكسور

= \frac{2}{1} \cdot \frac{3}{5} \cdot \frac{4}{5}

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

:اضرب كسور

= \frac{2 \cdot 3 \cdot 4}{1 \cdot 5 \cdot 5}

2 \cdot 3 \cdot 4 = 24 :

اضرب الأعداد

= \frac{24}{1 \cdot 5 \cdot 5}

1 \cdot 5 \cdot 5 = 25 :

اضرب الأعداد

= \frac{24}{25}

= \frac{24}{25}

أمثلة شائعة