What is the value of 2tan(π12)1tan2(π12)?

2 Answers
Nov 28, 2016

2tan(π12)1tan2(π12)=13

Explanation:

As tan(A+B)=tanA+tanB1tanAtanB

if A=B, we have tan2A=tanA+tanA1tanAtanA

or tan2A=2tanA1tan2A

Now putting A=π12

we have 2tan(π12)1tan2(π12)=tan(2×π12)=tan(π6)=13

Nov 28, 2016

Using identity tan2θ=2tanθ1tan2θ

we have the Expression

2tan(π12)1tan2(π12)

=tan(2×π12)=tan(π6)=13