Minimum 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.
Related questions
If cos θ = −1/2 and θ ∈ (π, 3π/2), then θ equals:tan(45° + θ) · tan(45° − θ) is equal to:sin 75° equals:By the law of sines in a triangle, a / sin A is equal to:The general solution of cos x = 0 is:The general solution of sin x = 0 is:If sin θ = 3/5 and θ is acute, then cos θ equals:The angle in radians for 120° is: