Trig Identities - where is my error?

Prove:

$\displaystyle csc(A)^2 + sec(A)^2 = csc(A)^2sec(A)^2$

left side is:

$\displaystyle (1/cos(A)^2) + (1/sin(A)^2)$

I multiply the first term by $\displaystyle (sin(A)^2)/(sin(A)^2)$

and the second term by $\displaystyle (cos(A)^2)/(cos(A)^2)$

$\displaystyle (sin(A)^2)/(sin(A)^2)(1/cos(A)^2) + (cos(A)^2)/(cos(A)^2)(1/sin(A)^2)$

Now the two terms have a common denominator and can be combined and we have:

$\displaystyle (sin(A)^2 + cos(A)^2)/(2cos(A)^2sin(A)^2)$

Then numerator = 1:

$\displaystyle 1/(2cos(A)^2sin(A)^2)$

Then we have

$\displaystyle (1/2)csc(A)^2sec(A)^2$

Where does the $\displaystyle 1/2$ come from? What am I doing wrong? How can I make the left side look like $\displaystyle csc(A)^2sec(A)^2$ ???

Thanx

-Tony