What is the value of cos(arctan(8/15)-arccos(3/5)) ?

The value of cos(arctan(8/15)-arccos(3/5)) is 77/85

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cos(arctan(8/15)-arccos(3/5))

cos (arctan (\frac{8}{15}) - arccos (\frac{3}{5}))

\frac{77}{85}

Solution steps

cos (arctan (\frac{8}{15}) - arccos (\frac{3}{5}))

Rewrite using trig identities:

cos (arctan (\frac{8}{15})) cos (arccos (\frac{3}{5})) + sin (arctan (\frac{8}{15})) sin (arccos (\frac{3}{5}))

= cos (arctan (\frac{8}{15})) cos (arccos (\frac{3}{5})) + sin (arctan (\frac{8}{15})) sin (arccos (\frac{3}{5}))

Rewrite using trig identities:

cos (arctan (\frac{8}{15})) = \frac{15}{17}

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arctan (\frac{8}{15})) = \frac{8}{17}

Rewrite using trig identities:

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

= \frac{15}{17} \cdot \frac{3}{5} + \frac{8}{17} \cdot \frac{4}{5}

Simplify

\frac{15}{17} \cdot \frac{3}{5} + \frac{8}{17} \cdot \frac{4}{5} : \frac{77}{85}

= \frac{77}{85}

sin (\frac{300}{2})

14 cos (3 0^{\circ})

csc (\frac{2}{3})

cot (\frac{π}{3}) - cos (\frac{π}{6})

- 8 sin (\frac{π}{2})

What is the value of cos(arctan(8/15)-arccos(3/5)) ?
The value of cos(arctan(8/15)-arccos(3/5)) is 77/85