I did this one differently. I went like...
left side
step one multiply by and then add because we've achieved a common denominator.
Then using the pythagorean identity, we can change into
Right side
convert the tan's into their proper sin and cosine values.
multiply by and add because we've achieved a common denominator.
factor out a
use the pythagorean identity to turn into 1
finally we end up with
L=R