What is the value of cos(arcsin(3/5)-arctan(5/12)) ?

The value of cos(arcsin(3/5)-arctan(5/12)) is 63/65

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cos(arcsin(3/5)-arctan(5/12))

cos (arcsin (\frac{3}{5}) - arctan (\frac{5}{12}))

\frac{63}{65}

Solution steps

cos (arcsin (\frac{3}{5}) - arctan (\frac{5}{12}))

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) cos (arctan (\frac{5}{12})) + sin (arcsin (\frac{3}{5})) sin (arctan (\frac{5}{12}))

= cos (arcsin (\frac{3}{5})) cos (arctan (\frac{5}{12})) + sin (arcsin (\frac{3}{5})) sin (arctan (\frac{5}{12}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arcsin (\frac{3}{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{63}{65}

= \frac{63}{65}

2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))

58 sin (5 4^{\circ})

\frac{67}{sin ( 4 5 ^{\circ} )}

tan (\frac{π}{4}) - sin (\frac{π}{6})

sec (- 31 0^{\circ})

What is the value of cos(arcsin(3/5)-arctan(5/12)) ?
The value of cos(arcsin(3/5)-arctan(5/12)) is 63/65