How do you prove #[(1+tan^(2)x )/ (tan^(2)x)]=csc^(2)x#?

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Answer 1 · 2016-09-18T07:47:01

Please see below.

As #1+tan^2x=sec^2x#

Hence #(1+tan^2x)/tan^x=sec^2x/tan^x#

= #(1/cos^2x)/(sin^2x/cos^2x)#

= #(1/cos^2x)xx(cos^2x/sin^2x)#

= #1/sin^2x#

= #csc^2x#