Question

Solve the following equation: (0,1) ✓2 Cos x + 1 = 0

Answer 1

The given equation is $\sqrt{2} \cos x+1=0$

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;

$\sqrt{2} \cos x=-1$

Dividing both sides by $\sqrt{2}$, we get;

$\cos x=-\frac{1}{\sqrt{2}}$

Rationalizing the equation, we have;

$\cos x=-\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2} }$

Simplifying, we get,

$\cos x=-\frac{\sqrt{2}}{2}$

The general solutions for $\cos x=-\frac{\sqrt{2}}{2}$ is $x=\frac{3 \pi}{4}+2 \pi n \ and \ x=\frac{5 \pi}{4}+2 \pi n$

Therefore, the solutions of the equation are $x=\frac{3 \pi}{4}+2 \pi n$ and $x=\frac{5 \pi}{4}+2 \pi n$