Question

Connections between tan theta and tan(90 + theta)

Answer 1

Tan(90+ theta)  = (tan90 + tantheta)/(1-tan90tantheta) 

= ( sin90costheta + sintheta cos 90) / (cos90costheta - sin90sintheta))
= sin(90 + theta)/ cos(90+  theta)  = costheta/-sintheta = - 1/tantheta


tan(90 + theta ) =  -1/tantheta