Question

Prove that
(1- tan theta / 1- cot theta )² = tan ² theta

Answer 1

Here I am using A instead of theta.

LHS =(1- tanA / 1- cot A )²

=[ (1-tanA)/(1-1/tanA)]²

= [(1-tanA)/{(tanA-1)/tanA}]²

=[(1-tanA)tanA]²/[-(1-tanA)]²

= [(1-tanA)²tan²A]/(1-tanA)²

After cancellation, we get

= tan²A

=RHS

••••