Question 61

Evaluate: $$(\sin 72^\circ + \cos 18^\circ) (\sin 72^\circ - \cos 18^\circ)$$

Solution

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$$ \sin72^\circ = \sin(90^\circ - 18^\circ) = \cos18^\circ $$

$$ (\sin(90^\circ - 18^\circ) + \cos18^\circ) (\sin(90^\circ - 18^\circ) - \cos18^\circ) $$

$$ (\cos18^\circ + \cos18^\circ) ( \cos18^\circ - \cos18^\circ) $$

$$ (\cos18^\circ + \cos18^\circ) \times 0 = 0 $$

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