Help please to simplify as far as possible? #(1-cos^2x)(1+cot^2x)#

1 Answer
Martin C.
Feb 26, 2018

#1#

Explanation:

#sin^2(x)+cos^2(x)=1|-cos^2(x)#
#sin^2(x)=1-cos^2(x)#
#cot^2(x)=cos^2(x)/sin^2(x)#
#(1-cos^2(x))(1+cot^2(x))#
#=sin^2(x)(1+cot^2(x))#
#=sin^2(x)(1+cos^2(x)/sin^2(x))#
#=sin^2(x)+cancel(sin^2(x))*cos^2(x)/cancel(sin^2(x))#
#=sin^2(x)+cos^2(x)#
#=1#

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