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If $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$,then $xy + yz + zx = $

Find the radian measure corresponding to the following degree measure: $-47^{\circ} 30^{\prime}$.

If $\sec \theta = \frac{13}{12}$ and $\theta$ lies in the $4^{\text{th}}$ quadrant,then $\tan \theta \times \operatorname{cosec} \theta \times \sin \theta \times \cos \theta = $

Evaluate: $\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$

$\sin 15^\circ + \cos 105^\circ = $

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