Question

establish the following equalities.

√3×tan60°-tan30°/1+tan60°×tan30°=1

Answer 1

Given tan60°-tan30°/1+tan60°-tan30°

It is in the form of (tanA - tanB)/(1 - tanA tanB) which is equal to tan(A - B) Hence tan60°-tan30°/1+tan60°-tan30° = tan(60° − 30°) = tan(30°) =1/√3

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