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

The value of cos(arcsin(4/5)-arctan(12/5)) is 63/65

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

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

\frac{63}{65}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{3}{5} \cdot \frac{5}{13} + \frac{4}{5} \cdot \frac{12}{13} : \frac{63}{65}

= \frac{63}{65}

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What is the value of cos(arcsin(4/5)-arctan(12/5)) ?
The value of cos(arcsin(4/5)-arctan(12/5)) is 63/65