Question

Evaluate the expression. 50 points!!

Answer 1

Answer:

2+2+2

Step-by-step explanation:

32+2+23

Answer 2

Answer:

C

Step-by-step explanation:

If you notice, this is what the tangent-difference identity resembles. The tangent-difference identity is:

$\tan(\alpha-\beta)=\frac{\tan(\alpha)-\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}$

We have the expression:

$\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}$

So, our α is π/7 and our β is π/8. Therefore:

$\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{\pi}{7}-\frac{\pi}{8}})$

Simplify:

$\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{8\pi}{56}-\frac{7\pi}{56}})$

Subtract:

$\frac{\tan(\frac{\pi}{7})-\tan(\frac{\pi}{8})}{1-\tan(\frac{\pi}{7})\tan(\frac{\pi}{8})}=\tan(\frac{\pi}{56})$

So, our answer is C.

And we're done!