あえて

Go through the trouble to…

あえて (敢えて) has 2 meanings:

1. “Go through the trouble to” – To do something regardless of the hardship or difficulty. This is the most common meaning. Equivalent to 無理をしてする、or わざわざ
2. To strengthen a negative. This is rare and mostly occurs in old writing. “no need to” “Not at all”.

Go through the trouble to

Sometimes said to mean “Dare to“.
May be used with positives or negatives.
Implies difficulty, futility, fear, or unexpectedness.
Implies a need for resolve.
Due to the implication of hardship, can be used like “forced themselves to”.

Examples

• 彼は敢て嬉しい顔をした
  He forced himself to make a happy face.
  
  
• 敢て上る必要はない
  There’s no reason to go through the trouble of climbing the mountain.
• 人が怖くて、あえて部屋から出ようとしない
  He’s scared of people, so instead (of going through the trouble), he doesn’t try to leave his room.
• その席ではあえて反対意見を言う者はいなかった (Weblio)
  No one dared to disagree at that place.
  
  
• メモを敢て日本語で書く
  Go through the trouble to write my notes in Japanese. 
  
  
• 単語を敢て調べずにそのままに読む
  Intentionally not look up a word and just read it as it is. 
  
  

Negatives

This is a rare usage. So rare in fact, its hard to find examples.
Going to give you one example for now because this is not an important usage.

Examples

• 敢て驚くにはあたらない (Weblio)
  No need to be surprised/Nothing to be surprised about.