Giúp mình nha gpt lượng giác

N

newstarinsky

a) ĐK...................
PT tương đuơng
$tan^25x(tan^22x.tan^23x-1)=(tan2x-tan3x)(tan2x+tan3x)\\
\Leftrightarrow tan^25x(tan2x.tan3x-1)(tan2x.tan3x+1)=\dfrac{(sin2x.cos3x-sin3x.cosx2x)}{cos2x.cos3x}.\dfrac{(sin2x.cos3x+sin3x.cos2x)}{cos2x.cos3x}\\
\Leftrightarrow tan^25x(\dfrac{(sin2x.sin3x-cos2x.cos3x)(sin2x.sin3x+cos2x.cos3x)}{cos^22x.cos^23x})=\dfrac{-sinx.sin5x}{cos^22x.cos^23x}\\
\Leftrightarrow tan^25x.(-cos5x).cosx=-sinx.sin5x\\
\Leftrightarrow sin^25x.cos5x.cosx=cos^25x.sin5x.sinx\\
\Leftrightarrow cos5x.sin5x(sin5x.cosx-cos5x.sinx)=0\\
\Leftrightarrow sin5x.cos5x.sin4x=0$
 
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