Question

find the value of

tan20°+tan40°+root3tan20°tan40°​

Answer 1

||✪✪ QUESTION ✪✪||

find the value of :- tan20°+tan40°+root3tan20°tan40° ?

|| ★★ FORMULA USED ★★ ||

• Tan(A+B) = [ (TanA + TanB) / ( 1 - TanA*TanB) ]
• Tan60° = √3

|| ✰✰ ANSWER ✰✰ ||

we can say that, Tan(60°) can be written as Tan(20°+40°) ...

→ Tan(20° + 40°)

Using above Told Formula now, Tan(A+B) = [ (TanA + TanB) / ( 1 - TanA*TanB) ] we get,

→ Tan(20° + 40°) = (Tan20° + Tan40°)/(1- Tan20° * Tan40°)

→ Tan(60°) = (Tan20° + Tan40°)/(1- Tan20° * Tan40°)

Cross - Multiply Now,

→ Tan60° - Tan60° * Tan20° * Tan40° = Tan20° + Tan40°

Putting Tan60° = √3 now,

→ √3 - √3 * Tan20° * Tan40° = Tan20° + Tan40°

Taking (-ve) part RHS, side now,

→ Tan20° + Tan40° + √3 * Tan20° * Tan40° = √3 (Ans).

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Answer 2

Answer:

Ans is root 3

Step-by-step explanation:

tan60=tan20+40

(tan20+tan40)/(1-tan20+tan40)

tan 60-tan60tan40/tan20+tan 40

=tan 20 +tan40+√3/tan20+tan40

=√3

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