How do you simplify the expression #(tan^2t+1)/(1+cot^2t)#?

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Answer 1 · 2016-08-29T06:54:19

#tan^2 t#.

The Exp.#=(tan^2 t+1)/(1+cot^2 t)#

#=(sin^2 t/cos^2 t+1)/(1+cos^2 t/sin^2 t)#

#={(cancel(sin^2 t+cos^2 t))/cos^2 t}/{cancel(cos^2 t+sin^2 t)/sin^2 t}#

#=sin^2 t/cos^2 t#

#=tan^2 t#.

Alternatively, to shorten the procedure of simplification, we can, use

the Identities # : tan^2 t+1=sec^2 t, and, 1+cot^2 t=csc^2 t#.