#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#