(2 cos 2a + 1) / (cos 2a + 1)

To simplify the expression (2 cos 2a + 1) / (cos 2a + 1), we can start by factoring out a common factor of 2 from the numerator:

(2 cos 2a + 1) / (cos 2a + 1) = (2(cos 2a) + 1) / (cos 2a + 1)

Now, we can see that the numerator is a sum of two terms, so we can split it into two separate fractions:

= (2(cos 2a) / (cos 2a + 1)) + (1 / (cos 2a + 1))

Next, we can simplify each fraction separately:

= 2(cos 2a) / (cos 2a + 1) + 1 / (cos 2a + 1)

Now, we can find a common denominator for the two fractions, which is (cos 2a + 1):

= (2(cos 2a) + 1) / (cos 2a + 1)

Finally, we can see that the numerator and denominator are the same, so the expression simplifies to:

= 1