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

1 Answer
Mar 9, 2018

See Below

Explanation:

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