AP EAMCET · Maths · Trigonometric Ratios & Identities
The maximum value of \(12 \sin x-5 \cos x+3\) is
- A \(18\)
- B \(13\)
- C \(16\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=12 \sin x-5 \cos x+3\) Now, \(-\sqrt{12^2+(-5)^2} \leq 12 \sin x-5 \cos x \leq \sqrt{12^2+(-5)^2}\) \(\begin{aligned} & \Rightarrow-13 \leq 12 \sin x-5 \cos x \leq 13 \\ & \Rightarrow-13+3 \leq 12 \sin x-5 \cos x+3 \leq 13+3\end{aligned}\)…
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