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Evaluate the expression

Evaluate the expression-example-1
User Wim
by
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1 Answer

3 votes

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)

User Yohannist
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