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Question

If a cosθ+b sinθ=4 and a sinθb cosθ=3, then a2+b2=___.

A
7
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B
12
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C
25
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D
None of these
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Solution

The correct option is C 25
a cosθ+b sinθ=4 and a sinθb cosθ=3
Squaring both the equations,
(a cosθ+b sinθ)2=42and (a sinθb cosθ)2=32Adding, we geta2cos2θ+2ab sinθcosθ+b2sin2θ+a2sin2θ2ab sinθcosθ+b2cos2θ=16+9a2(cos2θ+sin2θ)+b2(cos2θ+sin2θ)=25a2+b2=25

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