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Question
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
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Solution
`sin "A"/8 sin (3"A")/8 = 1/2(2 sin "A"/8 sin (3"A")/8)`
[∵ 2 sin A sin B = cos(A – B) – cos(A + B)
`= 1/2[cos ("A"/8 - (3"A")/8) - cos("A"/8 + (3"A")/8)]`
`= 1/2 [cos (("A" - 3"A")/8) - cos (("A" + 3"A")/8)]`
`= 1/2 [cos ((- 2"A")/8) - cos ("4A"/8)]`
`= 1/2 [cos ((- "A")/4) - cos ("A"/2)]`
`= 1/2 [cos "A"/4 - cos "A"/2]` ...[∵ cos(-θ) = cos θ]
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