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Prove the identity cosec A - 2*cot 2A * cos A = 2*sin A. Which statement is correct?

1. The identity is valid for all A where the functions are defined
2. It holds only when A = pi/2
3. The left side equals sin A, not 2 sin A
4. The identity is false

Correct answer: The identity is valid for all A where the functions are defined

Solution

Substituting cot2A and sin2A and using cos2A = 1 - 2sin² A, the left side collapses exactly to 2 sin A.

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