how would you simplify 2sin3xcosx=1

i've been stuck on this question for some time ;[

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- Jun 4th 2009, 08:58 PMwolfxpaxsimplifying trignometric identity
how would you simplify 2sin3xcosx=1

i've been stuck on this question for some time ;[ - Jun 4th 2009, 09:25 PMpickslides
consider $\displaystyle sin(a)cos(b) = \frac{1}{2}[sin(a+b)+sin(a-b)]

$

$\displaystyle 2sin(3x)cos(x)=1$

$\displaystyle 2(\frac{1}{2}[sin(3x+x)+sin(3x-x)])=1$

$\displaystyle sin(3x+x)+sin(3x-x)=1$

$\displaystyle

sin(4x)+sin(2x)=1

$