Given the expression:
[tex]sinx+cosx\cdot tanx=\sqrt{2}[/tex]
we have that tanx is equivalent to sinx/cosx, then, we have the following:
[tex]\begin{gathered} sinx+cosx(\frac{sinx}{cosx})=\sqrt{2} \\ \Rightarrow sinx+sinx=\sqrt{2} \\ \Rightarrow2sinx=\sqrt{2} \\ \Rightarrow sinx=\frac{\sqrt{2}}{2} \end{gathered}[/tex]
therefore, the simplified function is sinx = sqrt(2)/2
