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Prove that cot(A + 15 deg) - tan(A - 15 deg) = 4 cos(2A) / (1 + 2 sin(2A)).

1. Identity is true (proved)
2. Identity is false
3. RHS should be 4 cos 2A / (1 - 2 sin 2A)
4. RHS should be 2 cos 2A / (1 + 2 sin 2A)

Correct answer: Identity is true (proved)

Solution

Combining the fractions gives cos(A+15)cos(A-15) - sin(A+15)sin(A-15) over sin(A+15)cos(A-15). The numerator is cos(2A) shifted; simplification with product-to-sum identities gives 4 cos 2A/(1 + 2 sin 2A).

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