K
Find the expression that is equverchtin is $\frac{\operatorname{can} \frac{3 \pi}{5}+\tan \frac{\pi}{6}}{1-\tan \frac{3 \pi}{5} \tan \frac{\pi}{6}}$
Chouse the correct answer below
A. $\tan \frac{23 \pi}{30}$
B. $\tan \frac{13 \pi}{30}$
C. $\tan \frac{3 \pi}{5}+\tan \frac{\pi}{6}$
D. $\tan \frac{\pi}{10}$
Answer
Final Answer: The expression is equivalent to \(\tan \frac{23 \pi}{30}\), so the correct answer is \(\boxed{A. \tan \frac{23 \pi}{30}}\)
Step 1 ：The given expression is in the form of \(\frac{\tan a + \tan b}{1 - \tan a \tan b}\), which is equivalent to \(\tan(a+b)\). So, we need to find the sum of the angles \(\frac{3\pi}{5}\) and \(\frac{\pi}{6}\).
Step 2 ：Let a = \(\frac{\pi}{6}\) and b = \(\frac{3\pi}{5}\)
Step 3 ：Calculate the sum of the angles a and b, which is \(\frac{23\pi}{30}\)
Step 4 ：Final Answer: The expression is equivalent to \(\tan \frac{23 \pi}{30}\), so the correct answer is \(\boxed{A. \tan \frac{23 \pi}{30}}\)
