What is the value of sin(arcsin(4/5)-arctan(5/12)) ?

The value of sin(arcsin(4/5)-arctan(5/12)) is 33/65

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sin(arcsin(4/5)-arctan(5/12))

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

\frac{33}{65}

Solution steps

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{4}{5} \cdot \frac{12}{13} - \frac{3}{5} \cdot \frac{5}{13} : \frac{33}{65}

= \frac{33}{65}

47 sin (10 8^{\circ})

arcsin (- \frac{1}{6})

sec (- \frac{23 π}{6})

20 sin (7 0^{\circ})

- 5 + csc (e^{1 + 4})

What is the value of sin(arcsin(4/5)-arctan(5/12)) ?
The value of sin(arcsin(4/5)-arctan(5/12)) is 33/65