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Question
Without using trigonometric tables, prove that:
(sin 72° + cos 18°)(sin 72° – cos 18°) = 0
Theorem
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Solution
LHS=(sin72°+cos18°)(sin72°−cos18°)
=(sin72°+cos18°)[cos(90°−72°)−cos18°]
=(sin72°+cos18°)(cos18°−cos18°)
=(sin72°+cos18°)(0)
=0
=RHS
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Chapter 12: Trigonometric Ratios of Some Complemantary Angles - EXERCISE 12 [Page 590]
