anonymous
  • anonymous
Simplify asin(x/2)cos(x/2), is the answer sin2(x/2) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
asin?
anonymous
  • anonymous
$$\sin2\theta=2\sin\theta\cos\theta\implies\sin\theta\cos\theta=\frac12\sin2\theta$$Here, we have \(a\sin\frac{x}2\cos\frac{x}2=\frac{a}2\sin x\).
anonymous
  • anonymous
so... not sin2(x/2)

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anonymous
  • anonymous
Jeez that was a roundabout derivation @Mertsj :-p
Mertsj
  • Mertsj
@oldrin.bataku Sorry. I'll take it down. Didn't mean to offend you.
anonymous
  • anonymous
@Mertsj huh? no offense here! I just thought it was longer than needed :-p
anonymous
  • anonymous
We both came to the same result :-)
anonymous
  • anonymous
ok, sorry this is such a late response, but why is it (a/2)sinx rather than (a/2)sin2x.
Mertsj
  • Mertsj
You need to ask the genius @oldrin.bataku
anonymous
  • anonymous
@Cutiepo0 $$\sin2\theta=2\sin\theta\cos\theta\implies\sin\theta\cos\theta=\frac12\sin2\theta$$Understand so far? Now notice our expression can be treated as follows:$$a\sin\frac{x}2\cos\frac{x}2=a\left(\sin\frac{x}2\cos\frac{x}2\right)$$With \(\theta=x/2\), we observe that we apply our identity to yield:$$\sin\frac{x}2\cos\frac{x}2=\frac12\sin2\left(\frac{x}2\right)=\frac12\sin x$$Does that make sense so far? Now we put it all together:$$a\left(\sin\frac{x}2\cos\frac{x}2\right)=a\left(\frac12\sin x\right)=\frac12a\sin x$$

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