Question

Tan4π/5-tan2π/15+√3tan4pi/5tan2pi/15

Answer 1

• Given expression is equal to (-√3) .

To Find :- Value of Tan(4π/5) - tan(2π/15) + √3•tan(4π/5)•tan(2π/15) ?

Formula used :-

• tan(A - B) = [(tanA - tanB)/(1 + tanA•tanB)]
• tan(2π/3) = tan 120° = tan(90° + 30°) = - cot 30° = (-√3)

Solution :-

subtracting (2π/15) from (4π/5) we get :-

→ (4π/5) - (2π/15) = (12π - 2π)/15

→ (4π/5 - 2π/15) = (10π/15)

→ (4π/5 - 2π/15) = (2π/3)

multiply by tan both sides,

→ tan(4π/5 - 2π/15) = tan(2π/3)

→ tan(4π/5 - 2π/15) = (-√3)

using tan(A - B) = [(tanA - tanB)/(1 + tanA•tanB)] in LHS we get :-

→ [{tan(4π/5) - tan(2π/15)}/{1 + tan(4π/5)• tan(2π/15)}] = (-√3)

cross - multiply,

→ tan(4π/5) - tan(2π/15) = (-√3) - √3•tan(4π/5)• tan(2π/15)

→ tan(4π/5) - tan(2π/15) + √3•tan(4π/5)• tan(2π/15) = (-√3) (Ans.)

Hence, required value is equal to (-√3) .

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