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Question

If 2cosθ+sinθ=1(θπ2), then 7cosθ+6sinθ is equal to:

A
112
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B
465
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C
12
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D
2
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Solution

The correct option is D 2
2cosθ+sinθ=1 θπ2
2cosθ=1sinθ
4cos2θ=(1sinθ)2
Let sinθ=x
44x2=1+x22x
5x22x3=0
5x25x+3x3=0
(x1)(5x+3)=0
x=1sinθ=1θ=π2 but given θπ2
x=35
sinθ=35
cosθ=45
7cosθ+6sinθ=7×45+6×35=105=2

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