Question

prove that 1+tan^2θ/1+cot^2θ=(1−tanθ/1−cotθ)^2=tan^2θ

Answer 1

1 + tan^2titta = sec^2titta

1 + cot^2titta = cosec^2titta

so,

1 + tan^2titta/ 1 + cot^2titta = sec^2titta/cosec^2titta

=sin^2titta/cos^2titta

= tan^2titta

hence proved