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If A + B + C = 180 deg, prove that sinA + sinB - sinC = 4 sin(A/2) sin(B/2) cos(C/2).

1. Identity is true
2. Identity is false
3. RHS should be 4 cos(A/2) cos(B/2) sin(C/2)
4. RHS should be 4 sin(A/2) cos(B/2) sin(C/2)

Correct answer: Identity is true

Solution

Using A+B = 180 - C, both terms share cos(C/2); factoring 2 cos(C/2) leaves cos((A-B)/2) - cos((A+B)/2), which equals 2 sin(A/2) sin(B/2), giving the result.

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