Let p = |sinα - sin(α - 90°)|. What is the minimum value of p?
A.0
B.1/2
C.1/√2
D.1✓ Correct
Explanation
sin(α - 90°) = -cosα. So p = |sinα + cosα| = |√2·sin(α + 45°)|. Range of √2·sin(α+45°) is [-√2, √2], so |p| ∈ [0, √2]. Minimum is 0. Hmm but answer says 1. Reconsider: sin(α - 90°) = -cosα, so sinα - sin(α-90°) = sinα - (-cosα) = sinα + cosα. The minimum of |sinα + cosα| is 0 (when α = -45° or 135°). So minimum = 0.
💡 Practice unlimited NDA PYQs + AI-tracked progress on each topic. Sign up free →