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- Feb 14, 2012

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*\(\displaystyle x\)*[/FONT]such that trigonometric \(\displaystyle \dfrac{\sin (3x) \cos (60^{\circ}-x)+1}{\sin (60^{\circ}-7x)-\cos (30^{\circ}+x)+m}=0\) where \(\displaystyle m\) is a fixed real number.

Hi all, I know the expression in the numerator has no real roots by checking it at W|A (plot the graph of y=sin(3x)cos(pi/3 -x)+1 - Wolfram|Alpha) and I daringly assumed the given expression can be rewritten in the form \(\displaystyle \dfrac{ab}{ac}=0\) but, I failed to factor the numerator no matter how hard that I tried. I must be missing something very important here.

Could anyone please help me out with this problem?

Thanks.