# Evaluate ( limit as x approaches 0 of tan(x))/(tan(7x))

Apply trigonometric identities.
Rewrite in terms of sines and cosines.
Rewrite in terms of sines and cosines.
Multiply by the reciprocal of the fraction to divide by .
Simplify.
Convert from to .
Convert from to .
Consider the left sided limit.
Make a table to show the behavior of the function as approaches from the left.
As the values approach , the function values approach . Thus, the limit of as approaches from the left is .
Consider the right sided limit.
Make a table to show the behavior of the function as approaches from the right.
As the values approach , the function values approach . Thus, the limit of as approaches from the right is .
Evaluate ( limit as x approaches 0 of tan(x))/(tan(7x))