How do you simplify $sin(2sin^-1(10x))$ ?

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Answer 1 · 2017-10-28T08:35:16

$sin(2sin^(-1)10x)=20xsqrt(1-100x^2)$

Let $sin^(-1)10x=y$

then $siny=10x$ and $cosy=sqrt(1-(10x)^2)=sqrt(1-100x^2)$

and $sin(2sin^(-1)10x)$

= $sin(2y)$

= $2sinycosy$

= $2xx10x xxsqrt(1-100x^2)$

= $20xsqrt(1-100x^2)$

How do you simplify sin(2sin^-1(10x))sin(2sin^-1(10x))?