Calculate the value of the following expression: $$\frac{22(\sin^2 72^\circ - \cos^2 72^\circ)}{\cos 144^\circ}$$

Let's calculate the value of the given expression step by step. First, we can use the trigonometric identity $$\cos 2x = \cos^2 x - \sin^2 x$$. Therefore, $$-\cos 2x = \sin^2 x - \cos^2 x$$. In our case, we have: $$\sin^2 72^\circ - \cos^2 72^\circ = -\cos (2 \cdot 72^\circ) = -\cos 144^\circ$$ Now we can substitute this back into the original expression: $$\frac{22(\sin^2 72^\circ - \cos^2 72^\circ)}{\cos 144^\circ} = \frac{22(-\cos 144^\circ)}{\cos 144^\circ}$$ Since $$\cos 144^\circ
eq 0$$, we can cancel the $$\cos 144^\circ$$ terms: $$\frac{22(-\cos 144^\circ)}{\cos 144^\circ} = 22 \cdot (-1) = -22$$ Thus, the value of the expression is -22. Answer: -22