cos(6x)=cos(2x)
You asked:
Solve the equation \(\cos\left( 6 x \right) = \cos\left( 2 x \right)\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{\pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(\frac{1}{2} + n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.5707963\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(\frac{1}{4} + n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.78539816\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(3 + 4 n\right)}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 2.3561945\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]