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  4. The value of sec (2π/3)+cosec (5π/6) is equal to

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Q. The value of $sec \frac{2\pi}{3}+cosec \frac{5\pi}{6} $ is equal to

KEAMKEAM 2012

Solution:

$\sec \frac{2 \pi}{3}+\operatorname{cosec} \frac{5 \pi}{6}$
$=\sec \left(\pi-\frac{\pi}{3}\right)+\operatorname{cosec}\left(\pi-\frac{\pi}{6}\right)$
$=-\sec \frac{\pi}{3}+\operatorname{cosec}\left(\frac{\pi}{6}\right)=-2+2=0$