Recall that:
[tex]\tan x=\frac{\sin x}{\cos x}\text{.}[/tex]
Therefore:
[tex]\tan s=1\Leftrightarrow\frac{\sin s}{\cos s}=1.[/tex]
Then:
[tex]\sin s=\cos s\text{.}[/tex]
Now, notice that:
[tex]\sin s-\cos s=-\sqrt{2}\cos (s+\frac{\pi}{4}).[/tex]
Then:
[tex]-\sqrt[]{2}\cos (s+\frac{\pi}{4})=0.[/tex]
Therefore:
[tex]\cos (s+\frac{\pi}{4})=0.[/tex]
Then:
[tex]\begin{gathered} s+\frac{\pi}{4}=\frac{\pi}{2}+n\pi, \\ s+\frac{\pi}{4}=\frac{3\pi}{2}+n\pi\text{.} \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} s=\frac{\pi}{4}+n\pi, \\ s=\frac{5\pi}{4}+n\pi\text{.} \end{gathered}[/tex]
Since:
[tex]s\in\lbrack\pi,\frac{3\pi}{2}\rbrack^{},[/tex]
we get that:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]
Answer:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]
