Prove that 2cosx/cos2x+1=secx

1 answer

To prove that 2cosx / (cos2x + 1) = secx, we first need to simplify the left side of the equation.

We know that cos 2x = 2(cosx)^2 - 1. So, we substitute cos 2x with 2(cosx)^2 - 1 in the original equation.

2cosx / (2(cosx)^2 - 1 + 1)
= 2cosx / 2(cosx)^2

Now, we simplify further by dividing the numerator and denominator by 2cosx.

= 1 / cosx
= secx

Therefore, 2cosx / (cos2x + 1) is indeed equal to secx.