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Prove the trigonometric identity: [1 - cosA + cosB - cos(A+B)] / [1 + cosA - cosB - cos(A+B)] = tan(A/2)*cot(B/2).

1. Identity is true (LHS = tan(A/2)*cot(B/2))
2. Identity is false
3. LHS = tan(A/2)*tan(B/2)
4. LHS = cot(A/2)*cot(B/2)

Correct answer: Identity is true (LHS = tan(A/2)*cot(B/2))

Solution

Both numerator and denominator factor with common 2 sin((A+B)/2); after cancelling, numerator gives 2 sin(A/2) cos(B/2)-type product and denominator 2 cos(A/2) sin(B/2)-type product, whose ratio is tan(A/2) cot(B/2).

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