a)sin²x - 3sinx +2 =0
\(\left[ \begin{array}{l}sinx=2(loại)\\sinx=1\end{array} \right.\)
⇒x=$\frac{\pi }{2}$ +k2$\pi$ (k∈Z)
b)cot²3x - cot3x =0
\(\left[ \begin{array}{l}cotx=1\\cotx=0\end{array} \right.\)
\(\left[ \begin{array}{l}x=\frac{\pi }{2} +k\pi\\x=\frac{\pi}{4}+k\pi\end{array} \right.\) (k∈Z)
c) sin3x - $\sqrt{3}$ cos3x = -2
⇔ $\frac{1}{2}$ sin3x - $\frac{\sqrt{3} }{2}$ cos3x = -1
⇔sin3x.cos$\frac{\pi }{3}$ - cos3x.sin$\frac{\pi }{3}$ = -1
⇔sin(3x-$\frac{\pi }{3}$)=-1
⇔3x-$\frac{\pi }{3}$= -$\frac{\pi }{2}$+k2$\pi$
⇔x=-$\frac{\pi }{18}$+k$\frac{2}{3}$ $\pi$
d)cos3x + √3 sin3x=2
⇔$\frac{1}{2}$ cos3x + $\frac{\sqrt{3} }{2}$ sin3x = 1
⇔cos$\frac{\pi }{3}$.cos3x + sin$\frac{\pi }{3}$.sin3x=1
⇔cos($\frac{\pi }{3}$-3x)=1
⇔$\frac{\pi }{3}$-3x= k2$\pi$
⇒x=$\frac{\pi }{9}$-k$\frac{2}{3}$ $\pi$
