Sint * Cost = - 1/2
(SintCost)² = (- 1/2)²
Sin²tCos²t = 1/4
2 * Sin²t * Cos²t = 1/4 * 2
2Sin²tCos²t = 1/2
Sin⁴t + Cos⁴t = (Sin²t + Cos²t)² - 2Sin²tCos²t = 1 - 1/2 = 1/2
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Verified answer
Sint * Cost = - 1/2
(SintCost)² = (- 1/2)²
Sin²tCos²t = 1/4
2 * Sin²t * Cos²t = 1/4 * 2
2Sin²tCos²t = 1/2
Sin⁴t + Cos⁴t = (Sin²t + Cos²t)² - 2Sin²tCos²t = 1 - 1/2 = 1/2