$\cot x+\sin x\times\left ( 1+\tan x\times \tan \frac{x}{2} \right )=4$
Có $1+ tanx.tan\frac{x}2=1+\frac{sinx.sin\frac{x}2}{cosx.cos{x}2}$

$=\frac{sinx.sin\frac{x}2+cosx.cos\frac{x}2}{cosx.cos\frac{x}2}$

$=\frac{cos(x-\frac{x}2)}{cosx.cos\frac{x}2}$

$=\frac1{cosx}$

Thế vào $PT \Leftrightarrow \frac{cosx}{sinx}+\frac{sinx}{cosx}=4$

$\Leftrightarrow \frac{cos^2x+sin^2x}{sinxcosx}=4$

$\Leftrightarrow 4sinxcosx=1$

$\Leftrightarrow sin2x=\frac{1}2$

Còn lại bạn tự làm nha
Nếu đúng bạn nhấn V để chấp nhận, nhấn mũi tên để vote up cho đáp án của mình nha. Cảm ơn :) –  NguyễnTốngKhánhLinh 23-07-13 11:54 AM

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