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Question
Without using trigonometric tables, prove that:
tan48° tan23° tan42° tan67° = 1
Solution
LHS = tan 48° tan23° tan42° tan67°
= cost (90° - 48°) cost (90° - 23°) tan 42° tan 67°
= cot 42° cot 67° tan 42° tan 67°
`= 1/(tan 42°)xx1/(tan 67°)xxtan 42° xx tan 67°`
= 1
= RHS
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