SOLUTION: verify the identity of sin(x+y) + sin (x-y) = 2sin x cos y
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Question 1085650
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verify the identity of sin(x+y) + sin (x-y) = 2sin x cos y
Answer by
jim_thompson5910(35256)
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Use the following sum and difference identities to confirm the identity
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
Only alter the left side
sin(x+y) + sin(x-y) = 2*sin(x)*cos(y)
sin(x+y)
+ sin (x-y) = 2*sin(x)*cos(y)
sin(x)cos(y) + cos(x)sin(y)
+ sin (x-y) = 2*sin(x)*cos(y)
sin(x)cos(y) + cos(x)sin(y) +
sin(x-y)
= 2*sin(x)*cos(y)
sin(x)cos(y) + cos(x)sin(y) +
sin(x)cos(y) - cos(x)sin(y)
= 2*sin(x)*cos(y)
sin(x)cos(y) + cos(x)sin(y) + sin(x)cos(y) - cos(x)sin(y) = 2*sin(x)*cos(y)
[sin(x)cos(y) + sin(x)cos(y)] + [cos(x)sin(y) - cos(x)sin(y)] = 2*sin(x)*cos(y)
[2*sin(x)*cos(y)] + [0*cos(x)sin(y)] = 2*sin(x)*cos(y)
2*sin(x)*cos(y) = 2*sin(x)*cos(y)
The identity has been confirmed.
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