Tìm GTLN,GTNN của hàm số: y= $\frac{2 s i n x - 1}{c o s x + 2}$

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Tìm GTLN,GTNN của hàm số: y= $\frac{2 s i n x - 1}{c o s x + 2}$

Question

Tìm GTLN,GTNN của hàm số:
y= $\frac{2 s i n x - 1}{c o s x + 2}$

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Môn Toán Philomena 4 years 2020-10-13T15:29:38+00:00 2020-10-13T15:29:38+00:00 1 Answers 145 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Amity · Answer 1 · 2020-10-13T15:31:10+00:00

Amity

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2020-10-13T15:31:10+00:00 October 13, 2020 at 3:31 pm

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Đáp án:

$\begin{array}{l} y = \frac{2 \sin x - 1}{\cos x + 2} \\ \Rightarrow y . \cos x + 2 y = 2 \sin x - 1 \\ \Rightarrow y . \cos x - 2 \sin x = - 2 y - 1 \\ D k : y^{2} + {(- 2)}^{2} \geq {(- 2 y - 1)}^{2} \\ \Rightarrow y^{2} + 4 \geq 4 y^{2} + 4 y + 1 \\ \Rightarrow 3 y^{2} + 4 y - 3 \leq 0 \\ \Rightarrow \frac{- \sqrt{13} - 2}{3} \leq y \leq \frac{\sqrt{13} - 2}{3} \\ \Rightarrow {\begin{matrix} G T N N : y = \frac{- \sqrt{13} - 2}{3} \\ G T L N : y = \frac{\sqrt{13} - 2}{3} \end{matrix} \end{array}$

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