CircleMedium
Question
If a2 + b2 = 1, m2 + n2 = 1, then which of the following is true for all values of m, n, a, b -
Options
A.|am + bn| ≤ 1
B.| am - bn | ≥ 1
C.| am + bn | ≥ 1
D.| am - bn | ≤ 1
Solution
Consider a = cos θ, b = sin θ
m = cos φ, n = sin φ
Now, am ± bn = cos θ cos φ φ sin θ sin φ am + bn = cos (q ± θ)
∴ | am ± bn | ≤ 1
m = cos φ, n = sin φ
Now, am ± bn = cos θ cos φ φ sin θ sin φ am + bn = cos (q ± θ)
∴ | am ± bn | ≤ 1
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