Trigonometric Ratios Of Multiple And Sub Multiple Angles — Maths STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Multiple And Sub Multiple Angles1 Mark
Question
Write the maximum and minimum values of $3\cos\text{x}+4\sin\text{x}+5.$
✓
Answer
Let $\text{f(x)}=3\cos\text{x}+4\sin\text{x}+5$
We know that,
$-\sqrt{3^2+4^2}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{3^2+4^2}$
$\Rightarrow-\sqrt{9+16}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{9+16}$
$\Rightarrow-\sqrt{25}\le3\cos\text{x}+4\sin\text{x}\le\sqrt{25}$
$\Rightarrow-5\le3\cos\text{x}+4\sin\text{x}\le5$
$\Rightarrow-5+5\le3\cos\text{x}+4\sin\text{x}+5\le5+5$
$\Rightarrow0\le3\cos\text{x}+4\sin\text{x}+5\le10$
Hence, minimum and maximum value of $3\cos\text{x}+4\sin\text{x}+5$ are 0 and 10 respectively.
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