How do you solve and find the value of #cos(cos^-1(sqrt2/2)-pi/2)#?

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Answer 1 · 2018-04-07T18:18:49

#sqrt2/2#

First, recall that #cos(x-pi/2)=sinx#, so here, we're truly being asked to find

#sin(cos^-1(sqrt2/2))#

Now, determine #cos^-1(sqrt2/2)#.

#x=cos^-1(sqrt2/2) hArr cosx=sqrt2/2#, from the definition of an inverse function.

Keeping in mind that the domain of the inverse cosine is #[-1, 1],# the only solution to the above equation is

#x=pi/4#

Thus, we get

#sin(pi/4)=sqrt2/2#