Trig equivalence proof

[Ceebee]

Please prove the following:
Sin(a+b)-sin(a)=2cos(a+b/2)sin(b/2)
This is in Durrel & Robson elementary calculus vol 1 page 114.

 

[tkhunny]

Why are you in a calculus text without a sufficient background in trigonometry. You should fix that.

Is the cosine argument as you have written it, [math]a + \dfrac{b}{2}[/math], or was [math]\dfrac{a+b}{2}[/math] intended?

Expand sine and cosine of sums and see if anything strikes you.

 

[Deleted member 4993]

Please prove the following:
Sin(a+b)-sin(a)=2cos(a+b/2)sin(b/2)
This is in Durrel & Robson elementary calculus vol 1 page 114.

There are multiple formulae that can be used. Fundamentally, start with angle addition formula:

sin(a+b) = sin(a) * cos(b) + cos(a) * sin(b)

Please show us what you have tried and exactly where you are stuck.

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