The general solution of the equation $\cos x = \cos y$ is:

Question

Accepted Answer

If $\cos x = \cos y$, then $\cos x - \cos y = 0 \implies -2 \sin\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right) = 0$. This implies $\frac{x+y}{2} = n\pi$ or $\frac{x-y}{2} = n\pi$, which leads to $x = 2n\pi \pm y$, where $n \in \mathbb{Z}$.

Trigonometric Functions

❓ Sibling Questions in this Chapter