Sinx+cosx=2√2 sinxcosx

Sinx+cosx=2√2 sinxcosx

0 thoughts on “Sinx+cosx=2√2 sinxcosx”

  1. 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:

    $\sin x + \cos x = 2\sqrt2\sin x\cos x$

    $\Leftrightarrow \sqrt2\sin\left(x + \dfrac{\pi}{4}\right) = \sqrt2\sin2x$

    $\Leftrightarrow \sin\left(x + \dfrac{\pi}{4}\right) = \sin2x$

    $\Leftrightarrow \left[\begin{array}{l}x + \dfrac{\pi}{4} = 2x + k\pi\\x + \dfrac{\pi}{4} = \pi – 2x + k2\pi\end{array}\right.$

    $\Leftrightarrow \left[\begin{array}{l}x =  \dfrac{\pi}{4}+ k\pi\\x = \dfrac{\pi}{4} + k\dfrac{2\pi}{3}\end{array}\right.\quad (k\in\Bbb Z)$

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