If acosθ+bsinθ=4 and asinθ−bcosθ=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 acosθ+bsinθ=4 and asinθ−bcosθ=3
Squaring both the equations, (acosθ+bsinθ)2=42and(asinθ−bcosθ)2=32Adding, we geta2cos2θ+2absinθcosθ+b2sin2θ+a2sin2θ−2absinθcosθ+b2cos2θ=16+9⇒a2(cos2θ+sin2θ)+b2(cos2θ+sin2θ)=25⇒a2+b2=25