If the solutions for theta of cos ptheta + co | vedclass

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(B) Given $\cos p	heta = -\cos q	heta = \cos(\pi + q	heta)$.This implies $p	heta = 2n\pi \pm (\pi + q	heta)$ for $n \in \mathbb{Z}$.Case $1$: $p\

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$\frac{2\pi}{p + q}$

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(B) Given $\cos p	heta = -\cos q	heta = \cos(\pi + q	heta)$.This implies $p	heta = 2n\pi \pm (\pi + q	heta)$ for $n \in \mathbb{Z}$.Case $1$: $p	heta = 2n\pi + \pi + q	heta \implies 	heta = \frac{(2n + 1)\pi}{p - q}$. This forms an $A.P.$ with common difference $d_1 = \frac{2\pi}{|p - q|}$.Case $2$: $p	heta = 2n\pi - (\pi + q	heta) \implies 	heta = \frac{(2n - 1)\pi}{p + q}$. This forms an $A.P.$ with common difference $d_2 = \frac{2\pi}{p + q}$.Comparing the two,the numerically smallest common difference is $\frac{2\pi}{p + q}$.

If the solutions for $\theta$ of $\cos p\theta + \cos q\theta = 0$ with $p > 0, q > 0$ are in an $A.P.$,then the numerically smallest common difference of the $A.P.$ is

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