If $p = \cos{55{^\circ}},\ q = \cos{65{^\circ}}$ and $r = \cos 175{^\circ}$, then the value of $\frac{1}{p} + \frac{1}{q} + \frac{r}{pq}$ is

Question

Dr. Abubacker · Accepted Answer

(a)
$\frac{1}{p} + \frac{1}{q} + \frac{r}{pq} = \frac{p + q + r}{pq}$
$= \frac{\cos{55{^\circ} + \cos{65{^\circ} + \cos{175{^\circ}}}}}{\cos{55{^\circ}\cos{65{^\circ}}}}$
$= \frac{\cos{55{^\circ} + 2\cos\frac{175{^\circ} + 65{^\circ}}{2}}\cos\frac{175{^\circ} - 65{^\circ}}{2}}{\cos{55{^\circ}\cos{65{^\circ}}}}$
$= \frac{\cos{55{^\circ} + 2\cos{120{^\circ}}}\cos{55{^\circ}}}{\cos{55{^\circ}\cos{65{^\circ}}}} = \frac{1 - 2 	imes \frac{1}{2}}{\cos{65{^\circ}}} = 0$

Q. If $p = \cos{55{^\circ}},\ q = \cos{65{^\circ}}$ and $r = \cos 175{^\circ}$, then the value of $\frac{1}{p} + \frac{1}{q} + \frac{r}{pq}$ is

Explanation

Reviewed by Dr. Abubacker

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