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شائع علم المثلثات >

tan(arcsin(4/5)+arccos(1))

الحلّ

tan (arcsin (\frac{4}{5}) + arccos (1))

الحلّ

\frac{4}{3}

+1

عشري

1.33333 \dots

خطوات الحلّ

tan (arcsin (\frac{4}{5}) + arccos (1))

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{4}{5} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{4}{5} ) ) tan ( arccos ( 1 ) )}

tan (arcsin (\frac{4}{5}) + arccos (1))

tan (s + t) = \frac{tan ( s ) + tan ( t )}{1 - tan ( s ) tan ( t )}

:فعّل متطابقة الجمع لزوايا

= \frac{tan ( arcsin ( \frac{4}{5} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{4}{5} ) ) tan ( arccos ( 1 ) )}

= \frac{tan ( arcsin ( \frac{4}{5} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{4}{5} ) ) tan ( arccos ( 1 ) )}

Rewrite using trig identities:

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

tan (arcsin (\frac{4}{5}))

Rewrite using trig identities:

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

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}} :

استخدم المتطابقة التالية

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

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

بسّط

= \frac{4}{3}

Rewrite using trig identities:

tan (arccos (1)) = 0

tan (arccos (1))

Rewrite using trig identities:

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

tan (arccos (x)) = \frac{1 - x ^{2}}{x} :

استخدم المتطابقة التالية

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

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

بسّط

= 0

= \frac{\frac{4}{3} + 0}{1 - \frac{4}{3} \cdot 0}

بسّط

= \frac{4}{3}

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