Question

    If sin⁶  x + cos⁶  x = 7/8, find sin⁴  x +

    cos⁴  x:
    A 5/6 Correct Answer Incorrect Answer
    B 3/4 Correct Answer Incorrect Answer
    C 11/12 Correct Answer Incorrect Answer
    D 7/10 Correct Answer Incorrect Answer

    Solution

    We know that: sin⁶  x + cos⁶  x = (sin²  x + cos²  x)(sin⁴  x + cos⁴  x - sin²  x cos²  x). Since sin²  x + cos²  x = 1, We get: 1 × (sin⁴  x + cos⁴  x - sin²  x cos²  x) = 7/8. Now, let sin²  x cos²  x = z. So, sin⁴  x + cos⁴  x = 1 - 2z. From the equation 1 - 2z –z = 7/8, solving gives: 3z = 1 - 7/8 = 1/8, hence z = 1/24. Thus, sin⁴  x + cos⁴  x = 1 - 2 × 1/24 = 1 - 1/12 = 11/12. Correct option: c) 11/12

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