LHS = tan 225° cot 405° + tan 765° cot 675°

= tan (90° × 2 + 45°) cot (90° × 4 + 45°) + tan (90° × 8 + 45°) cot (90° × 7 + 45°)

We know that when n is odd, cot → tan.

= tan 45° cot 45° + tan 45° [-tan 45°]

= tan 45° cot 45° - tan 45° tan 45°

= 1 × 1 – 1 × 1

= 1 – 1

= 0

= RHS

Hence proved.