(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Simplify this expression.

sin(2* arcsin(x/3))

2. Relevant equations

3. The attempt at a solution

Let t = arcsin(x/3), we get sin(2t) which is double angle

sin(2T) = 2 sinT cosT

I did cosT first

T = arcsin x/3, and we know inverse of arcsin is sin T = x/3

this gives us the hypotenuse 3, and opposite side = x (3sin delta = x)

using the identity of cos^2 + sin^2 = 1, and solve for cos, I get cosT = sqrt(9-x^2)

This is corrected.

Now, solve for sinT.

sin(arcsin(x/3)), is the same as just x/3, by definition I think.

Well, the answer the book gave was 2x/9 * cosT

I get the cosT part right, but now the x/9

I don't understand how he produced the number 9.

Thank you. I have an exam so please pardon me posting so many questions these two days.

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