[Toán 11] Phương trình lượng giác

N

noinhobinhyen

Vì $sinx ; cosx \in [-1;1] \Leftrightarrow sin^{2012}x \leq sin^2x ; cos^{2012}x \leq cos^{2}x$


$\Rightarrow sin^{2012}x+cos^{2012}x \leq sin^2x+cos^2x=1$

Vậy thì $sin^{2012}x+cos^{2012}x = 1 \Leftrightarrow $

TH1 : $sinx = \pm 1 ; cosx = 0 \Leftrightarrow x=\dfrac{\pi}{2}+k\pi$



TH2 : $sinx = 0 ; cosx = \pm 1 \Leftrightarrow x=k\pi$
 
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