Note that the sin of an angle that will give a result of √2/2 are
[tex]\frac{1}{4}\pi\quad and\quad \frac{3}{4}\pi[/tex]
So we need to equate the angle to those value above.
From the problem, we have :
[tex]\sin (5x-\pi)=\frac{\sqrt[]{2}}{2}[/tex]
Equate the angle :
[tex]\begin{gathered} 5x-\pi=\frac{1}{4}\pi \\ 5x=\frac{1}{4}\pi+\pi \\ 5x=\frac{5}{4}\pi \\ x=\frac{5}{20}\pi=\frac{1}{4}\pi \end{gathered}[/tex][tex]\begin{gathered} 5x-\pi=\frac{3}{4}\pi \\ 5x=\frac{3}{4}\pi+\pi \\ 5x=\frac{7}{4}\pi \\ x=\frac{7}{20}\pi \end{gathered}[/tex]
The solutions are :
[tex]\mleft\lbrace\frac{\pi}{4},\frac{7\pi}{20}\mright\rbrace[/tex]
The answer is B.
