Question

Evaluate the expression

Answer 1

Answer: C)  tan(pi/56)

=============================================

Explanation:

I recommend using a trig identity reference sheet. The specific identity we will be using is $\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)} = \tan(A-B)$

What we are given is in the form $\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}$ with A = pi/7 and B = pi/8

A-B = (pi/7)-(pi/8)

A-B = pi(1/7-1/8)

A-B = pi(8/56 - 7/56)

A-B = pi*(1/56)

A-B = pi/56

Therefore,

$\frac{\tan\left(\pi/7\right)-\tan(\pi/8)}{1+\tan(\pi/7)\tan(\pi/8)} = \tan\left(\pi/56\right)$