Find the general solution of sinx + cosx =-1

1.	Find the general solution of sinx + cosx =-1
Answer» $\large\underline\purple{\bold{Solution :- }}$ $\tt \longrightarrow \: sinx \: + \: cosx = - 1$ ☆ on SQUARING both SIDES, we GET $\tt\implies \:{(sinx + cosx)}^{2} = {( - 1)}^{2}$ $\tt\implies \: {sin}^{2} x + {cos}^{2} x + 2 \: sinx \: cosx \: = 1$ $\tt\implies \:1 + sin2x = 1$ $\tt\implies \:sin \: 2x = 0$ $\tt\implies \:2x \: = n\pi$ $\tt\implies \:x = \dfrac{n\pi}{2} \: for \: every \: n \: is \: an \: integer.$

Answer»

$\large\underline\purple{\bold{Solution :- }}$