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))