Mathematics - Trigonometric Equation Question with Solution | TestHub

Given the equation:

$1+\cos (px)+1+\cos (qx)=2$

This simplifies to:

$$\cos \left(\frac{p+q}{2}\right)x\cos \left(\frac{p-q}{2}\right)x=0$$

This implies that $x=\frac{(2n+1)\pi }{p+q}$ or $x=\frac{(2n+1)\pi }{p-q}$ for $n=0,\pm 1,\pm 2,\dots$.

These solutions form an arithmetic progression (AP) with a common difference of $\frac{2\pi }{p+q}$ or $\frac{2\pi }{p-q}$.