1. $sin(x+30)=cos2x$
<=> $sin(x+\frac{π}{6})=sin(\frac{π}{2}-2x)$

( π = 180 độ, => 30 độ = $\frac{π}{6}$, vế kia thì anh dùng tính chất cung phụ)

<=> $\left[ \begin{array}{l}x+\frac{π}{6}=\frac{π}{2}-2x+k2π\\x+\frac{π}{6}=π-\frac{π}{2}+2x+k2π\end{array} \right.$ 

<=> $\left[ \begin{array}{l}3x=\frac{π}{6}+k2π\\-x=\frac{π}{6}+k2π\end{array} \right.$ 

<=> $\left[ \begin{array}{l}x=\frac{π}{18}+\frac{k2π}{3}\\x=-\frac{π}{6}-k2π\end{array} \right.$ 

2. $cos^{2}5x$=1

<=> $\frac{1+cos10x}{2}=1$

<=>$1+cos10x=2$

<=>$cos10x=1$
<=>$10x=k2π$

<=>$x=\frac{kπ}{5}$

3. $sin^{2}2x=\frac{9}{4}$ ( câu này có nhìu cách)

<=> $\frac{1-cos4x}{2}=\frac{9}{4}$

<=>$1-cos4x=\frac{9}{8}$

<=>$cos4x=-\frac{1}{8}$

<=>$cos4x=arccos(-\frac{1}{8})$

<=>$\left[ \begin{array}{l}4x=arccos(-\frac{1}{8})+k2π)\\4x=-arccos(-\frac{1}{8})+k2π)\end{array} \right.$

<=>$\left[ \begin{array}{l}x=\frac{arccos(-\frac{1}{8})}{4}+\frac{kπ}{2}\\x=-\frac{arccos(-\frac{1}{8})}{4}+\frac{kπ}{2}\end{array} \right.$ 

Chúc em học tốt!!