Question

Find the general solution of sinx + cosx =-1​

Answer 1

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

$\tt \longrightarrow \: sinx \: + \: cosx = - 1$

☆ on squaring both sides, we get

$\tt\implies \:{(sinx + cosx)}^{2} = {( - 1)}^{2}$

$\tt\implies \: {sin}^{2} x + {cos}^{2} x + 2 \: sinx \: cosx \: = 1$

$\tt\implies \:1 + sin2x = 1$

$\tt\implies \:sin \: 2x = 0$

$\tt\implies \:2x \: = n\pi$

$\tt\implies \:x = \dfrac{n\pi}{2} \: for \: every \: n \: is \: an \: integer.$