Question

Evaluate the expression

Answer 1

Answer: C) tan(pi/56)

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Step-by-step explanation:

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

What we are given is in the form
`(\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,

`(\tan\left(\pi/7\right)-\tan(\pi/8))/(1+\tan(\pi/7)\tan(\pi/8)) = \tan\left(\pi/56\right)`