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#.