Answer :
[tex]tan225^ocot405^o+cot675^otan765^o=0\\\\L=tan(180^o+45^o)cot(2\times180^o+45^o)+\dots\\\dots+cot(4\times180-45^o)tan(4\times180^o+45^o)\\\\=tan45^ocot45^o+cot(-45^o)tan45^o=1-cot45^otan45^o\\\\=1-1=0\\\\===================================\\\\tan\alpha\times cot\alpha=1\\\\cot(-\alpha)=-cot\alpha[/tex]
[tex]tan 225^0 cot 405^0 + cot 675^0 tan 765^0=\\=tan(180^0+45^0)\cdot cot(2\cdot180^0+45^0)+\\+cot(4\cdot180^0-45^0)\cdot tan(4\cdot180^0+45^0)=\\=tan45^0\cdot cot45^0-cot45^0\cdot tan45^0=1\cdot1-1\cdot1=1-1=0[/tex]
