Question

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

Answer 1

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

Explanation:

`"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))`