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Question

If L=(4tan1)(4tan2)(4tan3)(4tan10),M=(tan2)(tan4)(tan6)(tan20), and N=(1+tan1)(1tan1)(1+tan2)(1tan2)(1+tan10)(1tan10), then the value of L128MN is

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Solution

Given
L=(4tan1)(4tan2)(4tan3)(4tan10)M=(tan2)(tan4)(tan6)(tan20)N=(1+tan1)(1tan1)(1+tan2)(1tan2)(1+tan10)(1tan10)N=(1tan21)(1tan22)(1tan210)

We know that
tan2=2tan11tan21
So,
MN=210tan1tan2tan3tan10LMN=410210LMN=210L128MN=21027=8

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