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Question
Without using trigonometric tables, prove that:
cos54° cos36° − sin54° sin36° = 0
Solution
LHS = cos 54° cos36° - sin 54° sin 36°
= cos (90° - 36°) cos 36° - sin (90° - 360°) sin 36°
= sin 36° cos 36° - cos 36° sin 36°
= 0
= RHS
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