How do you prove 2 sin y cos x = sin (x + y) − sin (x − y) ?

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Answer 1 · 2018-03-06T07:20:45

As proved below.

Let’s simplify the R H S and prove equal to L H S.

Basic formulas of Trigonometry
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R H S #sin (x+y) - sin (x - y)#

Applying the above formulas and expand R H S.

#(sin x cos y + cos x sin y) - (sinx cos y - cos x sin y)#

#=> cancel(sin x cos y )+ cos x sin y - cancel(sin x cos y) + cos x sin y#

#=> 2 cos x sin y = L H S#

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