Question

I can only manipulate one side of the equation and the end result should be equal to the other side. please help.

((sinx + cosx)/(1 + tanx))^2 + ((sinx - cosx)/(1 - cotx))^2 = 1

Answer 1

since there's only one side that needs manipulating, I'd pick the left side. :-)

since
1+tan = (sin+cos)/cos and
1-cot = (sin-cos)/sin

we have

[(sin+cos)*cos/(sin+cos)]^2 + [(sin-cos)*sin/(sin-cos)]^2

= sin^2+cos^2
= 1