How do we simplify #(1 - tanx)/(1 - cotx)#?

1 Answer
Noah G
Apr 7, 2017

We simplify as follows, using the identities #tanx = sinx/cosx# and #cotx = cosx/sinx#.

#=(1 - sinx/cosx)/(1 - cosx/sinx)#

#=((cosx- sinx)/cosx)/((sinx - cosx)/sinx)#

#=(cosx - sinx)/cosx * sinx/(sinx - cosx)#

#=-(sinx - cosx)/cosx * sinx/(sinx - cosx)#

#=-sinx/cosx#

#=-tanx#

Practice Exercises

#1#. Simplify the following.

#(cotx + 1)/(tanx + 1)#

Solution

#=cotx#

Hopefully this helps!

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