## giải giúp e từng bước với ạ

Question

giải giúp e từng bước với ạ

in progress 0
1 year 2020-11-27T08:48:52+00:00 2 Answers 50 views 0

1. Đáp án: $$\left[ \begin{array}{l}x = \dfrac{π}{4} + k\dfrac{2π}{3}\\x = \dfrac{3π}{4} + k2π\end{array} \right.$$ (k ∈ ZZ)

Giải thích các bước giải:

sin (2x – π/4) = cos x

<=> sin (2x – π/4) = sin (π/2 – x)

<=> $$\left[ \begin{array}{l}2x – \dfrac{π}{4} = \dfrac{π}{2} – x + k2π\\2x – \dfrac{π}{4} = \dfrac{π}{2} + x + k2π\end{array} \right.$$

<=> $$\left[ \begin{array}{l}x = \dfrac{π}{4} + k\dfrac{2π}{3}\\x = \dfrac{3π}{4} + k2π\end{array} \right.$$ (k ∈ ZZ)

2. Đáp án:

$\begin{array}{l} \sin \left( {2x – \dfrac{\pi }{4}} \right) = \cos x\\ \Leftrightarrow \sin \left( {2x – \dfrac{\pi }{4}} \right) = \sin \left( {\dfrac{\pi }{2} – x} \right)\\ \Leftrightarrow \left[ \begin{array}{l} 2x – \dfrac{\pi }{4} = \dfrac{\pi }{2} – x + k2\pi \\ 2x – \dfrac{\pi }{4} = \pi – \left( {\dfrac{\pi }{2} – x} \right) + k2\pi \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} 3x = \dfrac{{3\pi }}{4} + k2\pi \\ 2x – \dfrac{\pi }{4} = \dfrac{\pi }{2} + x + k2\pi \end{array} \right.\\ \Rightarrow \left[ \begin{array}{l} x = \dfrac{\pi }{4} + \dfrac{{k2\pi }}{3}\\ x = \dfrac{{3\pi }}{4} + k2\pi \end{array} \right. \end{array}$