How do you find the exact value of $cos[ arctan (-4/3) - arcsin (3/5) ]$ ?

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Answer 1 · 2016-05-24T05:00:40

Zero.

You may use calculator
$tan x = -4/3$ --> $x = 126.86$ (or $-53.14$ )
$sin y = 3/5$ --> $y = 36^@86$
$x - y = 90^@$

$cos 90^@ = 0$

How do you find the exact value of cos[ arctan (-4/3) - arcsin (3/5) ]cos[ arctan (-4/3) - arcsin (3/5) ]?