What is the value of cos(arcsin(3/5)+arctan(12/5)) ?

The value of cos(arcsin(3/5)+arctan(12/5)) is -16/65

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cos(arcsin(3/5)+arctan(12/5))

cos (arcsin (\frac{3}{5}) + arctan (\frac{12}{5}))

- \frac{16}{65}

Solution steps

cos (arcsin (\frac{3}{5}) + arctan (\frac{12}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) cos (arctan (\frac{12}{5})) - sin (arcsin (\frac{3}{5})) sin (arctan (\frac{12}{5}))

= cos (arcsin (\frac{3}{5})) cos (arctan (\frac{12}{5})) - sin (arcsin (\frac{3}{5})) sin (arctan (\frac{12}{5}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= - \frac{16}{65}

cos (\frac{π}{4} - \frac{5 π}{6})

9 sin (\frac{π}{4}) + 9 cos (\frac{π}{4})

arccos (\frac{3}{14})

cos (2 (\frac{π}{4}))

arctan (\frac{5}{- 3})

What is the value of cos(arcsin(3/5)+arctan(12/5)) ?
The value of cos(arcsin(3/5)+arctan(12/5)) is -16/65