How do you simplify sin(cos1x)?

1 Answer
May 9, 2016

sin(cos1(x))=1x2

Explanation:

Let's draw a right triangle with an angle of a=cos1(x).

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As we know cos(a)=x=x1 we can label the adjacent leg as x and the hypotenuse as 1. The Pythagorean theorem then allows us to solve for the second leg as 1x2.

With this, we can now find sin(cos1(x)) as the quotient of the opposite leg and the hypotenuse.

sin(cos1(x))=sin(a)=1x21=1x2