接続・逆接N1
〜（よ）うとも、〜くとも
even if... / no matter how... / even though...
Structure
V-意志形 + とも；い形語幹 + くとも
Explanation
A classical remnant meaning even if...: V-volitional + とも, or i-adjective + くとも.
Examples
どんなに困難だろうとも、最後まで挑戦する。
No matter how difficult it is, I'll keep challenging myself to the end.
例え高かろうとも、必要なものは買う。
Even if it's expensive, I'll buy what I need.
Note
The literary form of ても, common in writing, often with どんなに or 例え.