Find the exact value of the given expression.

Question

(tan17pi/12 - tan pi/4) / (1+tan 17pi/12 tan pi/4)

can you help with this? i got the answer 1/ squareroot 3

Answer 1

I assume you used:

tan(A - B) = (tanA - tanB)/( 1 + tanAtanB)

then (tan17pi/12 - tan pi/4) / (1+tan 17pi/12 tan pi/4)
= tan(17π/12 - π/4)
= tan( 7π/6) or tan 210° ---> quad III
= 1/√3

Answer 2

You are correct!