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anonymous
 5 years ago
express the given sum or difference as a product of sines and/or cosines
sin x+sin3x
anonymous
 5 years ago
express the given sum or difference as a product of sines and/or cosines sin x+sin3x

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sin + sin = 2sin(1/2 sum)sin(1/2 difference) Take theta_1 = 3x and theta_2 = x. Then half the sum is 2x and half the difference is x. So you get\[\sin x + \sin 3x =2\sin 2x \sin x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But sin(2x)=2sin(x)cos(x), so you can go further:\[2\sin 2x \sin x=2.2\sin x \cos x \sin x =4\sin^2 x \cos x\]
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