How do you simplify $Cos[cos^-1 (3/5) - sin^-1 (-4/5)]$ ?

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Answer 1 · 2016-06-21T17:10:19

Let $a = cos^(-1)(3/5)$ . Then, $cos a = 3/5>0$ .a is in either 1st

quadrant or in the 4th. Accordingly, $sin a = +-4/5$ .

Let $b = sin^(-1)(-4/5)$ . Then, $sin b = -4/5>0$ .b is in either 3rd

quadrant or in the 4th. Accordingly, $cos b = +-3/5$ .

Now, the given expression is

$cos(a-b)=cos a cos b+sin a sin b$

$=((3/5)(+-3/5)-(+-4/5)((-4/5))$

$=(+-9+-16)/25$

$=+-1, +-7/25$ .

How do you simplify Cos[cos^-1 (3/5) - sin^-1 (-4/5)] Cos[cos^-1 (3/5) - sin^-1 (-4/5)] ?