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Question
Find the integrals of the function:
sin 4x sin 8x
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Solution
Let `I = int sin 4x sin 8x`
`= 1/2 int 2 sin 4x sin 8x dx`
`= 1/2 int (cos 4x - cos 12 x) dx` ....[∵ 2 sin A sin B = cos (A - B) - cos (A + B)]
`= 1/2 [1/4 sin 4x - 1/12 sin 12 x] + C`
`= 1/8 [sin 4x - 1/3 sin 12 x] + C`
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