verify: (1 + tan^2x)/(tan^2x) = csc^2x

We know the popular trigonometric identity,

Sin^2x+cos^2x = 1, Dividing by cos^2x both sides, we get:

(sinx/cosx)^2+1 = 1/cos^2. Or

tan^2x+1 = sec^2 x. Dividing both sides by tan^2x,

(tan^2x+1)/tan^2x = sec^2x/Tan^2x = (1/cos^2x)(cos^2x/sin^2x) = 1/sin^2x = sec^2x.