Simplify this function of Double Angles?

Question

$\frac{sin 6 x}{sin 2 x} - \frac{cos 6 x}{cos 2 x}$ $(sin6x)/(sin2x) - (cos6x)/(cos2x)$

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Answer 1 · 2017-04-02T17:54:33

2

the given expression can be added as $\frac{sin 6 x cos 2 x - sin 2 x cos 6 x}{sin 2 x cos 2 x}$ $(sin 6x cos 2x -sin 2x cos 6x)/(sin 2x cos 2x)$

The expression in the numerator is equivalent to sin (6x-2x)= sin 4x= 2 sin 2x cos 2x

the given expression is thus reduced to $\frac{2 sin 2 x cos 2 x}{sin 2 x cos 2 x}$ $(2 sin 2x cos 2x )/ (sin 2x cos 2x)$ = 2