Question

solve the following equation:
sin(x)+square root of 2=-sin(x)

Answer 1

\(\sin{x} + \sqrt{2} = -\sin{x}\)
\(\implies 2\sin{x} = -\sqrt{2}\)
\(\displaystyle \implies \sin{x} = \frac{1}{\sqrt{2}}\)

So, \(\displaystyle x = n\pi+(-1)^{n}\frac{\pi}{4}\), where \(n \in \bf{Z}\)