How to prove sin⁡(x−a)+sin⁡(x+a)=2sin⁡(x)cos⁡(a)?

Russell Gillen

Russell Gillen

Answered

2022-01-14

How to prove sin(xa)+sin(x+a)=2sin(x)cos(a)?

Answer & Explanation

Mary Herrera

Mary Herrera

Expert

2022-01-15Added 37 answers

HINT
sin(x+y)=sinxcosy+cosxsiny
sirpsta3u

sirpsta3u

Expert

2022-01-16Added 42 answers

Using sin(x+y)=sin(x)cos(y)+cos(x)sin(y) as suggested
This means that:
sin(x+a)=sin(x)cos(a)+cos(x)sin(a)
sin(xa)=sin(x)cos(a)+cos(x)sin(a)=sin(x)cos(a)cos(x)sin(a),
since cos(x)=cos(x) and sin(x)=sin(x)
Adding sin(xa) and sin(x+a) together gives,
sin(x+a)+sin(xa)=2sin(x)cos(a)

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