`1)` `sin(2x+45°)=1/2`
`<=>sin(2x+45°)=sin\ 30°`
`<=>`$\left[\begin{array}{l}2x+45°=30°+k360°\\2x+45°=180°-30°+k360°\end{array}\right.\ (k\in Z)$
`<=>`$\left[\begin{array}{l}2x=-15°+k360°\\2x=105°+k360°\end{array}\right. \ (k\in Z)$
`<=>`$\left[\begin{array}{l}x=-7,5°+k180°\\2x=52,5°+k180°\end{array}\right. \ (k\in Z)$
$\\$
`b)` `tan3x=\sqrt{3}` (*)
`ĐK: cos3x\ne 0<=>3x\ne π/2+kπ`
`<=>x\ne π/6+{kπ}/3\ (k\in ZZ)`
(*)`<=>tan3x=tan\ π/3`
`<=>3x=π/3 +kπ\ (k\in ZZ)`
`<=>x=π/9 +kπ/3\ (k\in ZZ)` (thỏa đk)
$\\$
`c)` `sin3x=cosx`
`<=>sin3x=sin(π/2-x)`
`<=>`$\left[\begin{array}{l}3x=\dfrac{π}{2}-x+k2π\\3x=π-(\dfrac{π}{2}-x)+k2π\end{array}\right. (k\in Z)$
`<=>`$\left[\begin{array}{l}4x=\dfrac{π}{2}+k2π\\2x=\dfrac{π}{2}+k2π\end{array}\right. (k\in Z)$
`<=>`$\left[\begin{array}{l}x=\dfrac{π}{8}+\dfrac{kπ}{2}\\x=\dfrac{π}{4}+kπ\end{array}\right. (k\in Z)$
$\\$
`d)` `cos(3x-π/3)={-\sqrt{2}}/2`
`<=>cos(3x-π/3)=cos\ {3π}/4`
`<=>$\left[\begin{array}{l}3x-\dfrac{π}{3}=\dfrac{3π}{4}+k2π\\3x-\dfrac{π}{3}=\dfrac{-3π}{4}+k2π\end{array}\right. (k\in Z)$
`<=>`$\left[\begin{array}{l}3x=\dfrac{13π}{12}+k2π\\3x=\dfrac{-5π}{12}+k2π\end{array}\right. (k\in Z)$
`<=>`$\left[\begin{array}{l}x=\dfrac{13π}{36}+\dfrac{k2π}{3}\\x=\dfrac{-5π}{36}+\dfrac{k2π}{3}\end{array}\right. (k\in Z)$
