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Rewrite sin(x+pi)+sin(x-pi) as a product.

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2 Answers

Method 3.
 
Use Sum-To-Product Identity:
 
sin(u) + sin(v) = 2 sin((u+v)/2) cos((u-v)/2)
 
sin(x+pi) + sin(x-pi) = 2 sin(x) cos(pi) = -2 sin(x)
Method 1.
sin(x+pi)+sin(x-pi)
= 2sin x cos pi, after expanding and collecting like terms
= -2sin x
 
Method 2.
sin(x+pi)+sin(x-pi)
= -sin x - sin x, using reference angle
= -2sin x