The given equation is [tex]\sqrt{2} \cos x+1=0[/tex]
We need to determine the solution of the equation.
Solution:
The solution of the equation can be determined by solving the equation for x.
Let us subtract both sides of the equation by 1.
Thus, we get;
[tex]\sqrt{2} \cos x=-1[/tex]
Dividing both sides by [tex]\sqrt{2}[/tex], we get;
[tex]\cos x=-\frac{1}{\sqrt{2}}[/tex]
Rationalizing the equation, we have;
[tex]\cos x=-\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2} }[/tex]
Simplifying, we get,
[tex]\cos x=-\frac{\sqrt{2}}{2}[/tex]
The general solutions for [tex]\cos x=-\frac{\sqrt{2}}{2}[/tex] is [tex]x=\frac{3 \pi}{4}+2 \pi n \ and \ x=\frac{5 \pi}{4}+2 \pi n[/tex]
Therefore, the solutions of the equation are [tex]x=\frac{3 \pi}{4}+2 \pi n[/tex] and [tex]x=\frac{5 \pi}{4}+2 \pi n[/tex]
