find the exact value of the expression cossin145 and rewrite

find the exact value of the expression cos(sin^-1(4/5)) and rewrite the expression sin(tan^-1(x)) as an algebraic expression in x.

cos ( sin^-1 (4/5))

let sin^-1 (4/5) = x

sin x = 4/5

cos x = 3/5

therefore , cos ( sin^-1 (4/5) = 3/5

sin ( tan^-1 (x))

let y = tan^-1 x

tan y = x

tan theta = perpendicular / base

hence , perpendicular = x , base = 1

hypotenuse = sqrt ( x^2 + 1 )

so, sin y = perpendicular / hypotenuse = x / sqrt (x^2+1)

sin( tan^-1 x) = x / sqrt (x^2+1)