Question

tan2π\5-tanπ\15-√3tan2π\5tanπ\15​

Answer 1

I hope it will help you

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Answer 2

• Given expression is equal to (√3) .

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

Formula used :-

• tan(A - B) = [(tanA - tanB)/(1 + tanA•tanB)]
• tan(π/3) = tan 60° = √3

Solution :-

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

→ (2π/5) - (π/15) = (6π - π)/15

→ (2π/5 - π/15) = (5π/15)

→ (2π/5 - π/15) = (π/3)

multiply by tan both sides,

→ tan(2π/5 - π/15) = tan(π/3)

→ tan(2π/5 - π/15) = √3

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

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

cross - multiply,

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

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

Hence, required value is equal to √3 .

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