Question
The maximum value of 3cos θ - 4 sinθ is
Answer: Option C
:
C
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:
C
Let 3 = rcosα, 4 = rsinα, so r = 5
f(θ) = r.(cosαcosθ+sinαsinθ) = 5.cos(θ−α)
∴ The maximum value of f(θ) = 5.1 = 5.
{Since the maximum value of cos(θ−α) = 1}.
Aliter: As we know that, the maximum value of asinθ+bcosθ is +√a2+b2 and the minimum value
is -√a2+b2. Therefore, the maximum value is (3cosθ+4sinθ) = + √32+(−4)2 = 5 and the minimum value is -5.
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