Question

Please teach me how to simplify down to one trig function.

Answer 1

Given the expression:

`sinx+cosx\cdot tanx=√(2)`

we have that tanx is equivalent to sinx/cosx, then, we have the following:

`\begin{gathered} sinx+cosx((sinx)/(cosx))=√(2) \\ \Rightarrow sinx+sinx=√(2) \\ \Rightarrow2sinx=√(2) \\ \Rightarrow sinx=(√(2))/(2) \end{gathered}`

therefore, the simplified function is sinx = sqrt(2)/2