How do you identify #tantheta/(1-cos^2theta)#?

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Answer 1 · 2017-01-30T00:38:32

The expression can be simplified to #secthetacsctheta#

First of all, apply the identity #sin^2theta + cos^2theta = 1 -> sin^2theta = 1 - cos^2theta#:

#=tantheta/sin^2theta#

Now convert #tantheta# to #sintheta/costheta#.

#=(sin theta/costheta)/sin^2theta#

#= sin theta/costheta * 1/sin^2theta#

#=1/(costhetasintheta)#

Apply the identities #1/costheta = sectheta# and #1/sintheta = csctheta#.

#=secthetacsctheta#

Hopefully this helps!