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What is the maximum value of a cos x + b sin x + c? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\rm \sqrt{a^2+b^2+c}\)
  2. \(\rm \sqrt{a^2+b^2}+c\)
  3. \(\rm \sqrt{a^2+b^2}-c\)
  4. \(\rm \sqrt{a^2+b^2}\)

Answer (Detailed Solution Below)

Option 2 : \(\rm \sqrt{a^2+b^2}+c\)
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Detailed Solution

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Explanation:

Since, maximum value of acosx + bsinx is \(\sqrt{a^2+b^2}\)

So maximum value of acosx + bsinx + c is \(\sqrt{a^2+b^2} +c\)

∴ Option (b) is correct.

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