Answer :

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.


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