What is the value of sin(arcsin(5/13)-arccos(-3/5)) ?

The value of sin(arcsin(5/13)-arccos(-3/5)) is -63/65

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sin(arcsin(5/13)-arccos(-3/5))

sin (arcsin (\frac{5}{13}) - arccos (- \frac{3}{5}))

- \frac{63}{65}

Solution steps

sin (arcsin (\frac{5}{13}) - arccos (- \frac{3}{5}))

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arccos (- \frac{3}{5})) = - \frac{3}{5}

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{5}{13} (- \frac{3}{5}) - \frac{12}{13} \cdot \frac{4}{5} : - \frac{63}{65}

= - \frac{63}{65}

1 - sin (\frac{5 π}{6})

\frac{2 tan ( \frac{3 π}{8} )}{1 - tan ^{2} ( \frac{3 π}{8} )}

arcsin (\frac{1}{1})

cos (\frac{13 π}{8})

arccos (- 0.88)

What is the value of sin(arcsin(5/13)-arccos(-3/5)) ?
The value of sin(arcsin(5/13)-arccos(-3/5)) is -63/65