1+(tanA/sinB)²/1+(tanA/sinC)²=1+(sinA/tanB)²/1+(sinA/tanC)²
No, this equation is not true.
as written, it is false, but if you do it right:
(1+(tanA/sinB)^2)/(1+(tanA/sinC)^2)=(1+(sinA/tanB)^2)/(1+(sinA/tanC)^2)
then it is true.
(1+(tanA/sinB)^2)/(1+(tanA/sinC)^2)=(1+(sinA/tanB)^2)/(1+(sinA/tanC)^2)
then it is true.