three constraints are:
l1 Tan@a + l2 == Sin@a/Cos[a]^2 + 1/Sin@a,
l1 + l2/Tan@a == 1/(Cos@a (Sin@a)^2), 0 < a < \[Pi]/2
Why can't the following code solve the range of l1+l2? How to compute it correctly?
Reduce[{l1 Tan@a + l2 == Sin@a/Cos[a]^2 + 1/Sin@a,
l1 + l2/Tan@a == 1/(Cos@a (Sin@a)^2), 0 < a < \[Pi]/2,
t == l1 + l2}, t, {l1, l2, a}, Reals] // FullSimplify
