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

1 Answer
Oct 5, 2016

see below

Explanation:

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

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

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

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

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

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

#=-tan^2 theta#

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

#=-sec^2theta +1#

#=1-sec^2 theta#

#=#Right Side