Question

How do you simplify the expression `(1/2)sin(2arcsin(x/5))`?

Answer 1

`1/25xsqrt(25-x^2), |x|<=5`

Explanation:

Let a = arc sin (x/5) in [-pi/2, pi/2]#, giving

`sin a = x/5 in [-1, 1] and positive cos a= sqrt(1-sin^2a)=1/5sqrt(25-x^2)`.

Given expression

`= 1/2 sin (2a) = (1/2)(2 sin a cos a )=1/25xsqrt(25-x^2)`