Question

how
tan A+tan(60+A)+tan (120+A)=3tan3A???????? how

Answer 1

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

 

Answer 2

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please refer to the attachment above


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