Choose the correct answer from the alternatives given :
Maximum value of 24sin $θ$ + 7cos $θ$ is

7

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17

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24

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25

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Solution

The correct option is D $25$
Maximum value of a sin $θ$ + b cos $θ$ = $\sqrt{a^{2} + b^{2}}$
Hence, maximum value of 24 sin $θ$ + 7 cos $θ$
$= \sqrt{(24)^{2} + (7)^{2}} = \sqrt{576 + 49} = \sqrt{625} = 25$

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