[tex]\sin a+\cos a=1\\
(\sin a+\cos a)^2=1^2\\
\sin^2a+2\sin a\cos a+\cos^2 a=1\\
\sin^2a+\cos^2 a+2\sin a\cos a=1\\
2\sin a\cos a=0\\
\sin 2a= 0\\
\tan2a=\frac{\sin2a}{\cos 2a}=0[/tex]
[tex]\frac{\sin a}{\cos a}=\sin a\\
\text{Valorile lui $a$ pentru care sinusul este 0 sunt solutii ale ecuatiei:}
\\
a=\pi\in(0,2\pi)\\
\text{Considerama $a\neq\pi$ ecuatia devine echivalenta cu}\\
\frac{1}{\cos a}=1\Rightarrow \cos a=1\Rightarrow a=2k\pi\notin(0,2\pi),\forall k\in\mathbb{Z}\\
\text{ In concluzie multimea solutiilor este: }S=\{\pi\}
[/tex]
