4 years ago

Prove the identity cos(x-y)-cos(x+y)=2sinx siny

Mathematics

1 answer:

True [87]4 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

Using the Addition/ Subtraction formulae for cosine

Consider the left side

cos(x - y) - cos(x + y)

= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

= 2sinxsiny = right side ⇒ proven

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