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Question

Which of the following cannot be the value of (7sinθ+24cosθ+7) ?

A
-9
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B
22
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C
-11
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D
33
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Solution

The correct option is B 33
7sinθ+24cosθ+7
=25(725sinθ+2425cosθ)+7
=25(sinαsinθ+cosαcosθ)+7
=25cos(αθ)+7
Here,
sinα=725
cosα=2425
Now, from the inequality,
1sin(α+θ)1
2525cos(αθ)25
25+725cos(αθ)+725+7
1825cos(αθ)+732
18(7sinθ+24cosθ+7)<32[7sinθ+24cosθ+7=25cos(αθ)+7]
Hence the value of (7sinθ+24cosθ+7) will only lie in the interval [18,32].
Since 33 does not lie in the interval [18,32], thus 33 cannot be the value of given expression.

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