Question

tan 20° + tan 40° + √3 tan 20° tan 40° is equal to​

Answer 1

Answer:

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Answer 2

We have 20 + 40 = 60

tan(60) = tan(20+40)

tan (A+B) = tan(A) + tan(B) / 1 - ( tanA × tan(B) )

now using this formula

tan60 = tan 20 + tan 40 / 1 - tan20 × tan40

tan60 ( 1 - tan20 × tan40 ) = tan20 + tan 40

tan60 - tan60×tan20×tan40 = tan20 + tan 40

√3 - √3 × tan20 × tan 40 = tan20 + tan40

tan20 + tan40 + √3 × tan20 tan40 = √3