Question #11672

1 Answer
Y
May 9, 2017

#cotx#

Explanation:

#(cot(x)-1)/(1-tan(x))#
Consider that #cot(x)=1/tan(x)#
#(1/tanx-1)/(1-tanx)#

Since in the numerator, #1=tanx/tanx#:

#(1/tanx-(tanx)/tanx)/(1-tanx)#

#=((1-tanx)/tanx)/(1-tanx)#

#=(1-tanx)/tanx*1/(1-tanx)#

The #1-tanx# cancel to give us:

#1/tanx=cot(x)#

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