## giải giúp e từng bước với ạ

Question

giải giúp e từng bước với ạ

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1 year 2020-11-27T08:51:47+00:00 1 Answers 48 views 0

## Answers ( )

1. Đáp án:

$\begin{array}{l} e)\left( {\cos \dfrac{x}{2} – 1} \right)\left( {5\sin 2x + 4} \right) = 0\\ \Rightarrow \left[ \begin{array}{l} \cos \dfrac{x}{2} – 1 = 0\\ 5\sin 2x + 4 = 0 \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} \cos \dfrac{x}{2} = 1\\ \sin 2x = – \dfrac{4}{5} \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} \dfrac{x}{2} = k2\pi \\ 2x = \arcsin \left( { – \dfrac{4}{5}} \right) + k2\pi \\ 2x = \pi – \arcsin \left( { – \dfrac{4}{5}} \right) + k2\pi \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} x = k4\pi \\ x = \dfrac{1}{2}\arcsin \left( { – \dfrac{4}{5}} \right) + k\pi \\ x = \dfrac{\pi }{2} – \dfrac{1}{2}\arcsin \left( { – \dfrac{4}{5}} \right) + k\pi \end{array} \right.\\ a)sin\left( {2x – \dfrac{\pi }{4}} \right).\left( {2\sin 3x + 1} \right) = 0\\ \Rightarrow \left[ \begin{array}{l} \sin \left( {2x – \dfrac{\pi }{4}} \right) = 0\\ \sin 3x = – \dfrac{1}{2} \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} 2x – \dfrac{\pi }{4} = k\pi \\ 3x = \dfrac{{ – \pi }}{6} + k2\pi \\ 3x = \dfrac{{7\pi }}{6} + k2\pi \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} x = \dfrac{\pi }{8} + \dfrac{{k\pi }}{2}\\ x = \dfrac{{ – \pi }}{{18}} + k\pi \\ x = \dfrac{{7\pi }}{{18}} + k\pi \end{array} \right. \end{array}$