How do you prove tan(90°+a)=-cot(a)?

1 Answer

We know that

tan(90+a)=sin(90+a)/(cos(90+a))=[sin90*cosa+cos90*sina]/[cos90*cosa-sin90*sina]= [cosa]/[-sina]=-cotatan(90+a)=sin(90+a)cos(90+a)=sin90cosa+cos90sinacos90cosasin90sina=cosasina=cota

Note sin90=1 , cos90=0sin90=1,cos90=0