+129852 As you have it wriiten, Shades, it's not an identity.....I think it's supposed to be....
[cot^2 x + sec^2 x + 1] / cot^2 x = sec^4 x break the left side up into sines/cosines
[cos^2x/sin^2x + 1/cos^2x + 1 ] / [cos^2x / sin^2x] =
[ cos^2x/sin^2x + 1/cos^2x + 1] * [ sin^2x/ cos^2x] = [ distribute the term in the 2nd brackets]
[1 + sin^2x/cos^4x + 1* (sin^2x / cos^2x)]
1 + sin^2/cos^4x + tan^2x =
1 + tan^2x + sin^2x/cos^4x [1 + tan^2x = sec^2x]
sec^2x + sin^2x/cos^4x [sec^2x = 1/cos^2x]
1/cos^2x + sin^2x/cos^4x [ get a common denominator of cos^4x]
[cos^2x]/cos^4x + sin^2x/cos^4x =
[cos^2x + sin^2x]/ cos^4x =
[1] / cos^4x =
sec^4x and this = the right side
