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

Question

8304 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T17:56:56

see below

#(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