find the equivalent algeberuc expresion for each compostion

find the equivalent algeberuc expresion for each compostion.

1. sin(arccos(x))

2. tan (arccos(x))

please show all your work.

Solution

1.sin(arccos x)

let arc cos x=t

cos t=x

sin t =sqrt(1-x²)

Therefore sin(arccos x)=sqrt(1-x²)

2.tan(arccos x)

let arccos x=u

cos u=x

tan u=sqrt(1-x²)/x

Therefore tan(arccos x)=sqrt(1-x²)/x