What is the value of cos(arcsin(5/13)-arctan(4/3)) ?

The value of cos(arcsin(5/13)-arctan(4/3)) is 56/65

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cos(arcsin(5/13)-arctan(4/3))

cos (arcsin (\frac{5}{13}) - arctan (\frac{4}{3}))

\frac{56}{65}

Solution steps

cos (arcsin (\frac{5}{13}) - arctan (\frac{4}{3}))

Rewrite using trig identities:

cos (arcsin (\frac{5}{13})) cos (arctan (\frac{4}{3})) + sin (arcsin (\frac{5}{13})) sin (arctan (\frac{4}{3}))

= cos (arcsin (\frac{5}{13})) cos (arctan (\frac{4}{3})) + sin (arcsin (\frac{5}{13})) sin (arctan (\frac{4}{3}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{12}{13} \cdot \frac{3}{5} + \frac{5}{13} \cdot \frac{4}{5} : \frac{56}{65}

= \frac{56}{65}

cos (\frac{π}{2} + π)

cos (arccos (- \frac{10}{13}))

arcsin (\frac{1}{10})

sin (π) - sin (- π)

cos (4 0^{\circ}) cos (2 0^{\circ}) - sin (4 0^{\circ}) sin (2 0^{\circ})

What is the value of cos(arcsin(5/13)-arctan(4/3)) ?
The value of cos(arcsin(5/13)-arctan(4/3)) is 56/65