alleryMinimum value of sin²θ + cos⁴θ:
A1
B3/4
C1/2
D1/4
Answer & Solution
Correct answer: B. 3/4
Let x = sin²θ.
Then cos²θ = 1 - x, cos⁴θ = (1-x)².
Expression = x + (1-x)² = x + 1 - 2x + x² = x² - x + 1. Derivative: 2x - 1 = 0
→ x = 1/2. Min value = 1/4 - 1/2 + 1 = 3/4.
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