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OTP to be sent to Change
Just expand the function ..
Tan A + (tan 60 + tan A )/(1-tan60.tanA) + (tan (120) + tan A )/(1-tan120.tanA)
tan A + [root(3) + tanA]/[1-root(3).tanA] + [ tan A - root(3) ] /[1 + root(3).tanA]
tanA + [ root(3) + 3.tanA + tanA + root(3).tan^2A + tanA - root(3) -root(3).tan^2A + 3.tanA ] / [ 1 - 3tan^2A ]
tanA + [ 8tanA] / [ 1-3tan^2A ]
[9tanA - 3.tan^3A ]/[1-3tan^2A]
= 3.tan3A ( eqaul to RHS )
Hence proved
Regards
Arun(askIITians forum expert)
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