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

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Answer 1 · 2015-07-03T18:41:25

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

$"Let " y=sin(2sin^(-1)(10x))$

Now, let $" "theta=sin^(-1)(10x)" "=>sin(theta)=10x$

$=>y=sin(2theta)=2sinthetacostheta$

Recall that: $" "cos^2theta=1-sin^2theta=>costheta=sqrt(1-sin^2theta)$

$=>y=2sinthetasqrt(1-sin^2theta)$

$=>y=2*(10x)sqrt(1-(10x)^2)=color(blue)(20xsqrt(1-100x^2))$

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