How do you simplify #sin(cos^-1(2/3)-sin^-1(2/3))#?

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Answer 1 · 2016-07-29T17:37:48

#1/9#

Use #sin^(-1)x+cos^(-1)x=pi/2#. Here, #x = 2/3#.

Let #cos^(-1)(2/3)=a#. Then #cos a = 2/3#.

Now, the given expression is

#sin(2a-pi/2)#

#=-cos 2a#

#=1-2cos^2a#

#=(1-8/9)#

#=1/9#