How do you verify #(1-tan^2x)/(1-cot^2x) = 1-sec^2x#?

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Answer 1 · 2016-10-03T18:45:46

see below

#(1-tan^x)/(1-cot^2x) = 1-sec^2x#

Left Side#=(1-tan^2x)/(1-cot^2x)#

#=(1-tan^2x)/(1-(1/tan^2x))#

#=(1-tan^2x)/((tan^2x-1)/tan^2x)#

#=(1-tan^2x) * (tan^2x/(tan^2x-1)) #

#=(1-tan^2x) * (tan^2x/-(1-tan^2x)) #

#=-tan^2x#

#=-(sec^2x-1)#

#=-sec^2x+1#

#=1-sec^2x#

#=# Right Side