What is the value of cos(arcsin(5/13)+arctan(4/3)) ?

The value of cos(arcsin(5/13)+arctan(4/3)) is 16/65

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cos(arcsin(5/13)+arctan(4/3))

cos (arcsin (\frac{5}{13}) + arctan (\frac{4}{3}))

\frac{16}{65}

Solution steps

cos (arcsin (\frac{5}{13}) + arctan (\frac{4}{3}))

Rewrite using trig identities:

cos (arcsin (\frac{5}{13})) cos (arctan (\frac{4}{3})) - sin (arcsin (\frac{5}{13})) sin (arctan (\frac{4}{3}))

= cos (arcsin (\frac{5}{13})) cos (arctan (\frac{4}{3})) - sin (arcsin (\frac{5}{13})) sin (arctan (\frac{4}{3}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arcsin (\frac{5}{13})) = \frac{5}{13}

Rewrite using trig identities:

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

cot (\frac{5}{12})

1 + sin (\frac{7 π}{4})

sin (- \frac{π}{6} - 2 ln (3 i))

6 + 3 cos (\frac{π}{2})

e^{\frac{π}{4}} sin (\frac{π}{4})

What is the value of cos(arcsin(5/13)+arctan(4/3)) ?
The value of cos(arcsin(5/13)+arctan(4/3)) is 16/65