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[Element hero Neos]

Giải phương trình

$3cosx(1-\sqrt{sinx})-cos2x=2\sqrt{sinx}.sin^2x-1$

[sharker]

 

  $3\cos x(1 - \sqrt {\sin x} ) - \cos 2x = 2\sqrt {\sin x} .{\sin ^2}x - 1$

   $\Leftrightarrow 3\cos x(1 - \sqrt {\sin x} ) = 2\sqrt {\sin x} .{\sin ^2}x - 1 + \cos 2x$

   $\Leftrightarrow 3\cos x(1 - \sqrt {\sin x} ) = 2\sqrt {\sin x} .{\sin ^2}x - 2{\sin ^2}x$

   $\Leftrightarrow 3\cos x(1 - \sqrt {\sin x} ) = 2\sin {x^2}(\sqrt {\sin x}  - 1)$

   $\Leftrightarrow (1 - \sqrt {\sin x} )(3\cos x + 2\sin {x^2}) = 0$

Edited by sharker, 06-08-2017 - 22:12.