Discussion
The value of \(4cos36^{o}cos72^{o}\) is equal to
Answer: A
The value is 1.
Use the known values \(\cos 36^\circ = \frac{\sqrt{5} + 1}{4}\) and \(\cos 72^\circ = \frac{\sqrt{5} - 1}{4}\).
\[ \begin{aligned} 4\cos 36^\circ\cos 72^\circ &= 4 \times \frac{(\sqrt{5} + 1)(\sqrt{5} - 1)}{16} \\ &= \frac{5 - 1}{4} = 1 \end{aligned} \]
Two options both read 2 in the paper; neither is correct. 0 would need one of the cosines to vanish, and \(\sqrt{2}\) has no connection with these angles.
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