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Question
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
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Solution
L.H.S = (sin A + sin B) + sin C
= `2sin ("A" + "B")/2 cos(("A" - "B")/2) + 2sin "C"/2 cos "C"/2`
= `2cos "C"/2[cos(("A" - "B")/2) + sin "C"/2]`
= `2cos "C"/2[cos(("A" - "B")/2) + cos ("A" + "B")/2]`
= `2cos "C"/2[2cos "A"/2 cos "B"/2]`
= `4cos "A"/2 cos "B"/2 cos "C"/2`
= R.H.S
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