Evaluate the value of tan 105 degrees

We have to find the value of tan 105 degrees

Solution

tan 105 can be expressed as

tan (105)= tan (60 +45)

We know that Tan(A + B) = (TanA + TanB)/(1-TanATanB)

tan 105° = Tan(60°+ 45°)

tan 105= (Tan60° + Tan45°)/(1-Tan 60° Tan45°)

Bys substituting the know values of tan 60 and tan 45 we get

tan 105° = (√3 + 1) / (1 – √3)

Answer

tan 105° = (√3 + 1) / (1 – √3)

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