Connections between tan theta and tan (90 + theta)

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