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 $(1+tan^2x)/tan^x=sec^2x/tan^x$

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

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

= $1/sin^2x$

= $csc^2x$

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