How do I solve (sec^2(x))+(csc^2(x))

I am really stuck on getting a common denominator. I get to 1/cos^2x+1/sin^2x , but than I can't figure out how to multiply the terms together to get a common denominator. I keep getting (cos^2x)(sin^2x)/(cos^2x)(sin^2x) , because I know I have to do the same to the top as I do to the bottom.
If someone could explain why I am doing wrong and solve the problem I would greatly appreciate it !
(I know that I am solving this wrong because it would simplify to 1, and that is not an option in my practice booklet.)

sec²(x) + csc²(x)

Convert into sin/cos:
1/cos²(x) + 1/sin²(x)

Multiply the first term by sin²(x)/sin²(x):
sin²(x)/[sin²(x)cos²(x)] + 1/sin²(x)

Multiply the second term by cos²(x)/cos²(x):
sin²(x)/[sin²(x)cos²(x)] + cos²(x)/[sin²(x)cos²(x)]

Add both terms, since they have a common denominator:
[sin²(x) + cos²(x)] / [sin²(x)cos²(x)]

The numerator can be reduced to 1:
1/[sin²(x)cos²(x)]

This can be rewritten as:
csc²(x)sec²(x)

Or as:
2/sin²(2x) = 2csc²(2x)

(sec^2(x))+(csc^2(x))
.....1..............1
=----------- + ------------
..cos^2(x).....sin^2(x)

...sin^2(x)+cos^2(x)
=------------------------------
.....cos^2(x)sin^2(x)

........1
=------------------------
....cos^2(x)sin^2(x)

.......1.............1
=-------------- ------------
....cos^2(x)..sin^2(x)

=sec^2(x)csc^2(x) answer//

1 / cos ² x + 1 / sin ² x

sin ² x + cos ² x
-------------------------
cos ² x sin ² x

1
---------------------
cos ² x sin ² x

sec ² x csc ² x

1/ cos^2 x + 1/sin^2 x

= (sin^2 x + cos^2 x)/ cos^2 x sin^2 x

= 1/cos^2 x sin^2 x

= 4/ (2sinx cosx)^2

= 4/(sin2x)^2

= 4 cosec^2 (2x)