Sinx + sin^2 x/2 = 1/2 Sinx + cosx = cosx/1- sin2x

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1. $\sin x+{\sin}^2\dfrac{x}{2}=\dfrac{1}{2}$

   $\Rightarrow \sin x+\dfrac{1-\cos x}{2}=\dfrac{1}{2}$

   $\Rightarrow \sin x-\dfrac{\cos x}{2}=0$

   $\Rightarrow \dfrac{2}{\sqrt 5}\sin x-\dfrac{1}{\sqrt5}\cos x=0$

   Đặt $\dfrac{2}{\sqrt5}=\cos\alpha$ và $\dfrac{1}{\sqrt5}=\sin \alpha$

   $\Rightarrow \cos \alpha\sin x-\sin \alpha\cos x=0$

   $\Rightarrow \sin(x-\alpha)=0$

   $\Rightarrow x-\alpha=k\pi$

   $\Rightarrow x=\alpha+k\pi,(k\in\mathbb Z)$

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