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How do you prove #(2 cos 3x)/(sin 4x - sin 2x)=cscx?

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May 21, 2015

f(x) = $\frac{2 cos 3 x}{sin 4 x - sin 2 x}$ $(2cos 3x)/(sin 4x - sin 2x)$

From trig identity -> (sin 4x - sin 2x) = 2cos 3x.sin x

$f (x) = \frac{2 cos 3 x}{2 cos 3 x . sin x}$ $f(x) = (2cos 3x)/(2cos 3x.sin x)$ = $\frac{1}{sin x}$ $1/sin x$ = csc x

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