How do you simplify #Cos(sin^-1 (-3/5) + cos^-1 (3/5))#?

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Answer 1 · 2016-05-19T15:28:55

#0, +-24/25#.

Let #a = sin^(-1) (-3/5)#.

Then, #sin a = -3/5<0#. So, a is in the 3rd quadrant or in the 4th.

Accordingly,

cos a = (- or +)(4/5).

Let #b = cos^(-1) (3/5)#.

Then, #cos b = 3/5>0.# So, b is in the 1st quadrant or in the 4th.

Accordingly, sin b = +- 4/5#.

Now, the given expression$ = cos ( a + b ) = cos a cos b - sin a sin b#

#= (- or +)(4/5)(3/5)-(-3/5)(+-4/5)#

#=(- or+)(12/25)+-12/25#

#=0, +-24/25#