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    Question

    The value of (1 + sin⁴ A – cos⁴ A) cosec² A

    is:
    A −2 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D −1 Correct Answer Incorrect Answer

    Solution

    To simplify (1 + sin⁴ A – cos⁴ A) cosec² A   Use cos4 A = (1- sin² A) ² = 1-2 sin² A + sin4 A. Substitute: 1+ sin A4 -cos4 A = 2 sin² A. The expression becomes: (2 sin² A) csc² A = 2 sin² A. (1 /sin2 A) = 2. Thus, the value is 2.

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