Question:
The maximum value of \(3\cos\theta+4\sin\theta\) is
The maximum value of \(3\cos\theta+4\sin\theta\) is
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The maximum value of \(a\cos x+b\sin x\) is \(\sqrt{a^2+b^2}\).
Updated On: May 7, 2026
- \(2\)
- \(4\)
- \(5\)
- \(1\)
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The Correct Option is C
Solution and Explanation
Step 1: The standard maximum value of \[ a\cos\theta+b\sin\theta \] is \[ \sqrt{a^2+b^2} \]
Step 2: Here, \[ a=3,\qquad b=4 \]
Step 3: Therefore, maximum value is: \[ \sqrt{3^2+4^2} \] \[ =\sqrt{9+16} \] \[ =\sqrt{25} \] \[ =5 \] \[ \boxed{5} \]
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