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

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Answer 1 · 2017-01-06T09:59:33

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

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

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

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