How do you use the sum or difference identities to find the exact value of tan(23π12)?

1 Answer
Nov 30, 2016

tan(23π12)=131+3

Explanation:

First note that 23π12=2ππ12

and as tan(x+2π)=tan(x), then:

tan(23π12)=tan(π12)

Now: 112=1314,

So:

tan(π12)=tan(π4π3)

Using:

tan(α+β)=tanαtanβ1+tanαtanβ

tan(23π12)=tan(π4)tan(π3)1+tan(π4)tan(π3)

tan(23π12)=131+3