Question

What is `cos(sin^-1(0.5))`?

Answer 1

`cos(sin^(-1)(0.5))=sqrt(3)/2`

Explanation:

Let `sin^(-1)(0.5)=x` then

`rarrsinx=0.5`

`rarrcosx=sqrt(1-sin^2x)=sqrt(1-0.5^2)=sqrt(1-(1/2)^2)=sqrt(3)/2`

`rarrx=cos^(-1)(sqrt3/2)=sin^(-1)(0.5)`

Now,

`rarrcos(sin^(-1)(0.5))=cos(cos^(-1)(sqrt3/2))=sqrt(3)/2`