Question
Download Solution PDFIf p2 + q2 = 1 and m2 + n2 = 1, then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
p2 + q2 = 1
m2 + n2 = 1
Formula used:
sin2θ + cos2θ = 1
cos(A + B) = cos A cos B - sin A sin B
-1 ≤ cos θ ≤ 1
Calculation:
Let
p = cos θ, q = sin θ
m = cos ϕ, n = sin ϕ
Therefore,
⇒ pm + qn = cos θ cos ϕ + sin θ sin ϕ
⇒ pm + qn = cos(θ - ϕ)
∵ -1 ≤ cos θ ≤ 1
⇒ -1 ≤ pm + qn ≤ 1
⇒ |pm + qn| ≤ 1
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