Răspuns:
Explicație pas cu pas:
[tex]tg\left(\dfrac{\pi}{8}+x\right)tg\left(\dfrac{\pi}{8}-x\right)+tg\left(\dfrac{\pi}{8}+x\right)+tg\left(\dfrac{\pi}{8}-x\right)=1\\tg\left(\dfrac{\pi}{8}+x\right)+tg\left(\dfrac{\pi}{8}-x\right)=1-tg\left(\dfrac{\pi}{8}+x\right)tg\left(\dfrac{\pi}{8}-x\right)\\\\\dfrac{tg\left(\dfrac{\pi}{8}+x\right)+tg\left(\dfrac{\pi}{8}-x\right)}{1-tg\left(\dfrac{\pi}{8}+x\right)tg\left(\dfrac{\pi}{8}-x\right)}=1\\tg\left(\dfrac{\pi}{8}+x+\dfrac{\pi}{8}-x\right)=1\\tg\dfrac{\pi}{4}=1\\1=1,\texttt{adevarat}[/tex]
