How do you simplify cos(sin^-1x)?

2 Answers
Aug 11, 2017

After using u=Arcsin(x) or x=sinu transforms,

cos(arcsinx)

=cosu

=sqrt[1-(sinu)^2]

= sqrt(1-x^2)

Aug 11, 2017

costheta=sqrt(1-x^2)

Explanation:

cos(sin^-1x)

Let sin^-1x=theta

Then, x=sintheta

Now put the value for x in cos(sin^-1x)

=>cos(sin^-1(sintheta))

So the equation becomes,

=>costheta

We know that sin^2theta+cos^2theta=1

=>cos^2theta=1-sin^2theta

=>costheta=sqrt(1-sin^2theta)

We have already found that x=sintheta, then x^2=sin^2theta. Now put x^2 in the place for sin^2theta.

costheta=sqrt(1-x^2)