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Question
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
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Solution
cos(60° + A) sin(120° + A)
`= 1/2` [2 cos(60° + A) sin(120° + A)] ....[Multiply and divide by 2]
= `1/2` [sin((60° + A) + (120° + A))] – sin((60° + A) – (120° + A))] ....[∵ 2 cos A sin B = sin(A + B) – sin(A – B)]
= `1/2` [sin(180° + 2A) – sin(60° + A – 120° – A)]
= `1/2` [(-sin 2A) – sin(-60°)]
= `1/2` [-sin 2A + sin 60°]
= `1/2 [-sin 2"A" + sqrt3/2]`
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