Question

Prove that tan 225 cot 405 + cot 675 tan 765 = 0

Answer 1

`tan225^ocot405^o+cot675^otan765^o=0\\\\L=tan(180^o+45^o)cot(2*180^o+45^o)+\dots\\\dots+cot(4*180-45^o)tan(4*180^o+45^o)\\\\=tan45^ocot45^o+cot(-45^o)tan45^o=1-cot45^otan45^o\\\\=1-1=0\\\\===================================\\\\tan\alpha* cot\alpha=1\\\\cot(-\alpha)=-cot\alpha`