csc(tan^-1(10/9))
Draw a right angled trianle
mark one of the acute angles as theta
let
theta = inv tan (10/9)
that is
tan (theta) = 10/9
put 10 on the opposite side and 9 on the adjacent side
Use pythagoras theorem to find the hypotenuse
cosec=1/sin = hyp/opp
csc(tan^-1(10/9)) = sqr(181)/9