Question
If sin x + cos x = 7/5, find sin⁴ x + cos⁴
x:Solution
sin⁴ x + cos⁴ x = (sin² x + cos² x)² - 2sin² x cos² x sin² x + cos² x = 1, and (sin x + cos x)² = 1 + 2sin x cos x = 49/25 So, 2sin x cos x = 24/25 Now, sin² x cos² x = (12/25)² = 144/625 Thus, sin⁴ x + cos⁴ x = 1 - 2 * 144/625 = 1 - 288/625 = 337/625 Correct option: d
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