Write the following as an algebraic expression in x x 0 1 s

Write the following as an algebraic expression in x, x > 0.

1) sin(arcsin x/sqrt 3)

Solution

sin(arcsin x/sqrt3)

arc sinx= sin^-1x

sin (sin^-1 x/sqrt3)

Let sin^-1 x/sqrt3 = t

sin t= x/sqrt 3

Therefore sin(sin^-1x/sqrt3) = x/sqrt3 = xsqrt3/3