# How do you simplify Cos(arcsin (2x^3))?

reqd. value $= \sqrt{1 - 4 {x}^{6}}$
Suppose that $\arcsin \left(2 {x}^{3}\right) = \theta$, so that, by defn. of $\arcsin , \sin \theta = 2 {x}^{3}$
Now, reqd. value $= \cos \left(\arcsin 2 {x}^{3}\right) = \cos \theta = \sqrt{1 - {\sin}^{2} \theta} = \sqrt{1 - {\left(2 {x}^{3}\right)}^{2}} = \sqrt{1 - 4 {x}^{6}}$.