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Is the trigonometric identity cot⁴(A) + cot²(A) = cosec⁴(A) - cosec²(A) valid for all admissible values of A?

1. Yes, it is an identity true for all admissible A
2. No, it holds only when A = 45 deg
3. No, it holds only when cot(A) = 0
4. No, the two sides are never equal

Correct answer: Yes, it is an identity true for all admissible A

Solution

Both sides reduce to the same expression, so the equation is a genuine identity holding for every A where the functions are defined.

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