Sinx+cosx=2√2 sinxcosx Question Sinx+cosx=2√2 sinxcosx in progress 0 Môn Toán Khang Minh 4 years 2020-10-29T15:18:57+00:00 2020-10-29T15:18:57+00:00 1 Answers 133 views 0
Answers ( )
Đáp án:
$\left[\begin{array}{l}x = \dfrac{\pi}{4}+ k\pi\\x = \dfrac{\pi}{4} + k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in\Bbb Z)$
Giải thích các bước giải:
$\sin x + \cos x = 2\sqrt2\sin x\cos x$
$\Leftrightarrow \sqrt2\sin\left(x + \dfrac{\pi}{4}\right) = \sqrt2\sin2x$
$\Leftrightarrow \sin\left(x + \dfrac{\pi}{4}\right) = \sin2x$
$\Leftrightarrow \left[\begin{array}{l}x + \dfrac{\pi}{4} = 2x + k\pi\\x + \dfrac{\pi}{4} = \pi – 2x + k2\pi\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{4}+ k\pi\\x = \dfrac{\pi}{4} + k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in\Bbb Z)$