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Question
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
Solution
L.H.S. = tan 10° tan 15° tan 75° tan 80°
= tan 10° tan 15° tan (90° - 15°) tan (90° - 10°)
= = tan 10° tan 15° cot 15° cot 10°
= `1/cot 10° xx 1/cot 15° xx cot 15° xx cot 10°`
= 1
= RHS
Hence proved.
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