Question

Simplify the expression sin(2(sin^-1)(2/3)

Answer 1

sin(2 sin^-1 2/3)

= sin(sin^-1(2 x 2/3 \(\sqrt{1-(\frac23)^2}))\) (∵ 2 sin^-1 x \(=sin^{-1}(2x\sqrt{1-x^2}))\)

= sin(sin^-1(4/3 x √5/3))

\(=\frac{4\sqrt5}9\)