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

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

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

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

- \frac{33}{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{33}{65}

= - \frac{33}{65}

2 sec^{2} (\frac{π}{3})

sin (- \frac{5 π}{2})

sin (\frac{1}{2})

arccos (cos (- \frac{3 π}{5}))

2 sin (\frac{7 π}{6})

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