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Question

Prove that tan 6tan 42tan 66tan 78=1

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Solution


LHS = tan 6 tan 42 tan 66 tan 78
tan x tan (60 - x) tan (60 + x) = tan x - (standard fomula)
Let x = 18
tan18tan(6018)tan(60+18)=tan n(3×18)
tan 18 tan 42 tan 78 = tan 54
tan 42 tan 78 = tan 54tan 18
Let x = 6
tan 6 tan(60 - 6) tan (60 + 6) = tan 18
tan 6 tan 54 tan 66 = tan 18
tan6 tan 66=tan54tan18×tan18tan54=1
Hence proved

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