Giải phương trình 1.Sin(π/2 – x)=1 2.sin(x/2 –π/3)=–1 3.sin(π/2 – x)=1 4.sin(2x + 60°)=sin(x+1)

1. $sin\Bigg(\dfrac{\pi}{2}-x\Bigg)=1$

$↔ \dfrac{\pi}{2}-x=\dfrac{\pi}{2}+k2\pi$

$↔ x=k2\pi$ $(k∈Z)$

2. $sin\Bigg(\dfrac{x}{2}-\dfrac{\pi}{3}\Bigg)=-1$

$↔ \dfrac{x}{2}-\dfrac{\pi}{3}=-\dfrac{\pi}{2}+k2\pi$

$↔ x=-\dfrac{\pi}{3}+k4\pi$ $(k∈Z)$

4. $sin(2x+60^o)=sin(x+1)$

$↔ \left[ \begin{array}{l}2x+\dfrac{\pi}{3}=x+1+k2\pi\\2x+\dfrac{\pi}{3}=-x+k2\pi\end{array} \right.$

$↔ \left[ \begin{array}{l}x=1-\dfrac{\pi}{3}+k2\pi\\x=-\dfrac{\pi}{9}+\dfrac{k2\pi}{3}\end{array} \right.$ $(k∈Z)$