Answer: C) tan(pi/56)
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Explanation:
I recommend using a trig identity reference sheet. The specific identity we will be using is [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)} = \tan(A-B)[/tex]
What we are given is in the form [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}[/tex] 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,
[tex]\frac{\tan\left(\pi/7\right)-\tan(\pi/8)}{1+\tan(\pi/7)\tan(\pi/8)} = \tan\left(\pi/56\right)[/tex]
