Question

Find the value of `sin(cos^(-1)(x/2))`?

Answer 1

`sin(cos^(-1)(x/2))=sqrt(4-x^2)/2`

Explanation:

Let `cosA=x/2`, then `A=cos^(-1)(x/2)`

and `sinA=sqrt(1-cos^2A)=sqrt(1-(x/2)^2)`

= `sqrt((4-x^2)/4)=sqrt(4-x^2)/2`

Hence `sin(cos^(-1)(x/2))=sqrt(4-x^2)/2`