Question

7.
Prove that tan 20° + tan 40° + √3 tan 20° tan 40º = √3.​

Answer 1

we have 20+ 40=60

so tan 60 = tan ( 20 + 40 )

= ( tan 20 + tan 40 ) / ( 1 - tan 20 tan 40)

or tan 60 - tan 60 tan 20 tan 40 = tan 20 + tan 40

or root 3 - root 3 tan 20 tan 40 = tan 20 + tan 40

or tan 20 + tan 40 + root 3 tan 20 tan 40 = root 3

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