Consider the following for the three (03) items that follow: Let p...

Given p = \sin 35^{}^{\circ}, q = \sin 25^{}^{\circ}, and r = \sin(-95^{}^{\circ}).

We need to find the value of $p + q + r$.

p + q = \sin 35^{}^{\circ} + \sin 25^{}^{\circ}

Using the formula $\sin A + \sin B = 2 \sin \left(\dfrac{A+B}{2}\right) \cos\left(\dfrac{A-B}{2}\right):<br><br>$p + q = 2 \sin \left(\dfrac{35^{}^{\circ} + 25^{}^{\circ}}{2}\right) \cos\left(\dfrac{35^{}^{\circ} - 25^{}^{\circ}}{2}\right)$<br><br>$p + q = 2 \sin 30^{}^{\circ} \cos 5^{}^{\circ}$<br><br>Since$\sin 30^{}^{\circ} = \dfrac{1}{2}$:<br><br>$p + q = 2 \left(\dfrac{1}{2}\right) \cos5^{}^{\circ} = \cos 5^{}^{\circ}$<br><br>Now, evaluating$r$:<br><br>$r = \sin(-95^{}^{\circ}) = -\sin 95^{}^{\circ}$<br><br>$r = -\sin(90^{}^{\circ} + 5^{}^{\circ}) = -\cos 5^{}^{\circ}$<br><br>Therefore,$p + q + r = \cos 5^{}^{\circ} - \cos 5^{}^{\circ} = 0$<br><br>Answer:$0