What is the value of sin(arccos(4/5)-arctan(5/12)) ?

The value of sin(arccos(4/5)-arctan(5/12)) is 16/65

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sin(arccos(4/5)-arctan(5/12))

sin (arccos (\frac{4}{5}) - arctan (\frac{5}{12}))

\frac{16}{65}

Solution steps

sin (arccos (\frac{4}{5}) - arctan (\frac{5}{12}))

Rewrite using trig identities:

sin (arccos (\frac{4}{5})) cos (arctan (\frac{5}{12})) - cos (arccos (\frac{4}{5})) sin (arctan (\frac{5}{12}))

= sin (arccos (\frac{4}{5})) cos (arctan (\frac{5}{12})) - cos (arccos (\frac{4}{5})) sin (arctan (\frac{5}{12}))

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arctan (\frac{5}{12})) = \frac{12}{13}

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arctan (\frac{5}{12})) = \frac{5}{13}

= \frac{3}{5} \cdot \frac{12}{13} - \frac{4}{5} \cdot \frac{5}{13}

Simplify

\frac{3}{5} \cdot \frac{12}{13} - \frac{4}{5} \cdot \frac{5}{13} : \frac{16}{65}

= \frac{16}{65}

sec^{2} (18 0^{\circ})

tan^{2} (4 5^{\circ} - \frac{18}{2})

sin (- 76 5^{\circ})

\frac{0.4}{sin ( 3 0 ^{\circ} )}

\frac{100}{cos ( 6 0 ^{\circ} )}

What is the value of sin(arccos(4/5)-arctan(5/12)) ?
The value of sin(arccos(4/5)-arctan(5/12)) is 16/65