How do you verify the identity #1/(1-tan^2theta)+1/(1-cot^2theta)=1#?

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Answer 1 · 2018-03-09T18:38:49

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#LHS : 1/(1-tan^2theta) + 1/(1-cot^2theta)#

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

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

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

#=1/(1-tan^2theta) - tan^2 theta/(1-tan^2 theta)#->factor out -1

#=(1 - tan^2 theta)/(1-tan^2 theta)#->common denominator

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

#=1#

#=RHS#