What is the value of cos(arcsin(4/5)+arctan(5/12)) ?

The value of cos(arcsin(4/5)+arctan(5/12)) is 16/65

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cos(arcsin(4/5)+arctan(5/12))

cos (arcsin (\frac{4}{5}) + arctan (\frac{5}{12}))

\frac{16}{65}

Solution steps

cos (arcsin (\frac{4}{5}) + arctan (\frac{5}{12}))

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arcsin (\frac{4}{5})) = \frac{4}{5}

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

Simplify

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

= \frac{16}{65}

arcsec (- 7)

cot (\frac{10 π}{3})

tan (18 0^{\circ}) - 2 cos (18 0^{\circ}) + 3 csc (27 0^{\circ}) + sin (9 0^{\circ})

sin (20 5^{\circ})

\frac{7}{tan ( 3 0 ^{\circ} )}

What is the value of cos(arcsin(4/5)+arctan(5/12)) ?
The value of cos(arcsin(4/5)+arctan(5/12)) is 16/65