What is the value of sin(arcsin(5/13)+arccos(-4/5)) ?

The value of sin(arcsin(5/13)+arccos(-4/5)) is 16/65

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sin(arcsin(5/13)+arccos(-4/5))

sin (arcsin (\frac{5}{13}) + arccos (- \frac{4}{5}))

\frac{16}{65}

Solution steps

sin (arcsin (\frac{5}{13}) + arccos (- \frac{4}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{5}{13})) cos (arccos (- \frac{4}{5})) + cos (arcsin (\frac{5}{13})) sin (arccos (- \frac{4}{5}))

= sin (arcsin (\frac{5}{13})) cos (arccos (- \frac{4}{5})) + cos (arcsin (\frac{5}{13})) sin (arccos (- \frac{4}{5}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= \frac{16}{65}

sec (34 5^{\circ})

arccos (sin (\frac{3 π}{4}))

cos (\frac{π}{9}) cos (\frac{2 π}{9}) - sin (\frac{π}{9}) sin (\frac{2 π}{9})

csc (3 9^{\circ})

24 tan (7 0^{\circ})

What is the value of sin(arcsin(5/13)+arccos(-4/5)) ?
The value of sin(arcsin(5/13)+arccos(-4/5)) is 16/65