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Answer 1 · 2017-04-24T01:12:51

$sin 7 x cos x - cos 7 x sin x = sin (6 x)$ $Sin 7x cos x - cos 7x sin x = sin(6x)$

We have:

$sin 7 x cos x - cos 7 x sin x$ $Sin 7x cos x - cos 7x sin x$

We can use the sine sum of two angles formula:

$sin (A - B) \equiv sin A cos B - cos sin B$ $sin(A-B) -= sinAcosB - cossinB$

so that:

$sin 7 x cos x - cos 7 x sin x = sin (7 x - x)$ $Sin 7x cos x - cos 7x sin x = sin(7x-x)$
$= sin (6)$ $" " = sin(6)$