\(sina+cosa=\sqrt{2}\)
=>\(\sqrt{2}sin\left(a+\dfrac{pi}{4}\right)=\sqrt{2}\)
=>\(sin\left(a+\dfrac{pi}{4}\right)=1\)
=>\(a+\dfrac{pi}{4}=\dfrac{pi}{2}+k2pi\)
=>\(a=\dfrac{pi}{4}+k2pi\)
\(sina=sin\left(\dfrac{pi}{4}+k2pi\right)=\dfrac{\sqrt{2}}{2}\)
\(cosa=cos\left(\dfrac{pi}{4}+k2pi\right)=\dfrac{\sqrt{2}}{2}\)
\(tana=tan\left(\dfrac{pi}{4}+k2pi\right)=1\)
\(cota=\dfrac{1}{tana}=1\)