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

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

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