Question Summary:
If a man gives his wife 1 talaq and they reconcile is that talaq still valid?

Question Detail:

 
If a man gives his wife 1 talaq and they reconcile is that talaq still valid?, also how does a women go about divorcing her husband in shariah 

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
If a husband issues his wife one talaq and he revokes the talaq, the marriage will be reconstituted without a reperformance of a new nikah. However, the revoked talaq will not be defaced. This means the husband’s rights of talaq has decreased from three to two. He does not have the right of three divorces as before. The one talaq issued will be counted.
Almighty Allah Ta’ala has given the husband the rights to issue divorce. A wife cannot issue divorce. However, she may offer to make Khula if she wishes to discontinue the marriage.
Khula is if the wife is unhappy in the marriage, she may offer her husband the return of the Mahr in exchange of him divorcing her. If he agrees, then the Khula will be valid and it will constitute one talaq-e-baain.(1)(2)
And Allah Ta’āla Knows Best
Zakir Husain

Student DarulIftaa
Michigan, U.S.A
Checked and Approved by,
Mufti Ebrahim Desai.
 
 اذا تشاق الزوجان وخافا ان لاييقيما حدود الله لا باس ان تفتدي نفسها منه بمال يخلعها به (قدوري ص233 سعيد  (١)
 
من وقع على بينه وبين زوجته شقاق فله ان يطلقها على جغل ياخزه منها (مختصر طحاوى ج4 ص454 دار السراج      
  (٢)وأما ركنه فهو كما في البدائع : إذا كان بعوض الإيجاب والقبول لأنه عقد على الطلاق بعوض ، فلا تقع الفرقة ، ولا يستحق العوض بدون القبول (رد المحتار ، ج 3 ، 441 ، ايج ايم سعيد )