Re: Verify a trig identity

There may be an easier way, but if you convert the right hand side to be all in terms of (x/2) it works out pretty easily. Start with:

$\displaystyle \sin (2x) = \sin (\frac x 2 + \frac {3x} 2) = \sin (\frac x 2 ) \cos (\frac {3x} 2) + \cos (\frac x 2 ) \sin (\frac {3x} 2 )$

then apply the identities:

$\displaystyle \cos (3a) = \cos^3(a) - 3 \sin^2 (a) \cos(a)$

$\displaystyle \sin(3a) = 3 \cos^2(a) \sin (a) - \sin^3(a) $

using a = x/2.

You should end up with the right hand side being: $\displaystyle 2 \sin (\frac x 2) \cos ( \frac x 2)$, which is equivalent to $\displaystyle \sin (2 \times \frac x 2) = \sin(x) $

Re: Verify a trig identity

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Re: Verify a trig identity

You can also consider the attached solution.

Attachment 28658