Question

Find the exact value of tan (arcsin (2/5)). For full credit, explain your reasoning.

Answer 1

Since arcsin(2/5)=x, sin x=2/5

Here we go
`=sinx/(sqrt(1-sin^2x)) =(2/5)/(sqrt(1-4/5))`

`tan x = sinx/cosx`
More than one way possible :

`tan(arcsin(2/5)) =(2/5)/ (sqrt(21)/5)=2/sqrt(21)`