How do you find the exact value of #Cos[sin^-1(1/3) - arcsin(1/2)]#?

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How do you find the exact value of #Cos[sin^-1(1/3) - arcsin(1/2)]#?

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Answer 1 · 2016-05-26T15:00:21

#1/6 + sqrt(2/3)#

Explanation:

First we will consider that #sin^{-1} equiv arcsin#. We will need the identity
#cos(a-b)=cos(a)cos(b)+sin(a)sin(b)# and also that
#cos(arcsin(x))=sqrt(1-x^2)#. With all this in mind
#cos(arcsin(1/3)-arcsin(1/2))=1/6 + sqrt(2/3)#

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How do you find the exact value of #Cos[sin^-1(1/3) - arcsin(1/2)]#?

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