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Evaluate:

(1) $\dfrac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\tan 225^{\circ} \cdot \cos 200^{\circ}}$

(2) $\dfrac{\sin 36^{\circ}}{\sin 12^{\circ}}-\dfrac{\cos 36^{\circ}}{\cos 12^{\circ}}$
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(1)
$\begin{array}{ll} \frac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\tan \left(180^{\circ}+45^{\circ}\right) \cdot \cos \left(180^{\circ}+20^{\circ}\right)} & \text { (reduce angles to acute angles ) } \\ =\frac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\tan 45^{\circ} \cdot\left(-\cos 20^{\circ}\right)} & \left(\cos 20^{\circ}=\cos \left(90^{\circ}-70^{\circ}\right)=\sin 70^{\circ}\right) \\ =\frac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{(1) \cdot\left(-\sin 70^{\circ}\right)} & \left(70^{\circ} \text { is double } 35^{\circ}\right) \\ =\frac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\left(-\sin \left[2\left(35^{\circ}\right)\right]\right)} & \text { (apply the double angle formula) } \\ =\frac{\sin 35^{\circ} \cdot \cos 35^{\circ}}{\left(-2 \sin 35^{\circ} \cdot \cos 35^{\circ}\right)} & \\ =-\frac{1}{2} & \end{array}$

(2)
\begin{aligned} & \frac{\sin 36^{\circ} \cdot \cos 12^{\circ}}{\sin 12^{\circ} \cdot \cos 12^{\circ}}-\frac{\cos 36^{\circ} \cdot \sin 12^{\circ}}{\sin 12^{\circ} \cdot \cos 12^{\circ}} \quad\left(\mathrm{LCD}: \sin 12^{\circ} \cdot \cos 12^{\circ}\right) \\ & =\frac{\sin 36^{\circ} \cdot \cos 12^{\circ}-\cos 36^{\circ} \cdot \sin 12^{\circ}}{\sin 12^{\circ} \cdot \cos 12^{\circ}} \\ & =\frac{\sin \left(36^{\circ}-12^{\circ}\right)}{\sin 12^{\circ} \cdot \cos 12^{\circ}} \\ & =\frac{\sin 24^{\circ}}{\sin 12^{\circ} \cdot \cos 12^{\circ}} \\ & =\frac{\sin \left[2\left(12^{\circ}\right)\right]}{\sin 12^{\circ} \cdot \cos 12^{\circ}} \\ & =\frac{2 \sin 12^{\circ} \cdot \cos 12^{\circ}}{\sin 12^{\circ} \cdot \cos 12^{\circ}}=2 \end{aligned}
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