A 35-year-old lady with post coital bleeding management is:
Patient is 35 years old and presenting with post coital bleeding - raises the suspicion of cervical cancer because

CIN is usually asymptomatic. - CGDT 10th /ed p 836
Ca cervix presents with watery; blood tinged vaginal discharge. Intermittent vaginal bleeding that follows coitus i.e. post coital bleeding is a very specific symptom of cervical cancer.
Now in patients suspected of having cervical cancer, management is:
"In those with suspected cervical cancer, a thorough external genital and vaginal examination should be should be performed, looking for concomitant lesions"     ... Williams Gynae 1st /ed p 653
So the first step should be thorough clinical and vaginal examination.

Papanicolaou Smear —
"Histologic evaluation of cervical biopsy is the primary tool used to diagnose cervical cancer.
Although pap smears are performed extensively to screen for this cancer, this test does not always detect cervical cancer. Specifically,
Pap smear testing has only a 55- 80% sensitivity for detecting high grade, lesions on any given single test. Thus, the preventive power of Pap smear testing lies in a regular serial screening.
Moreover, in women who have stage-I cervical cancer, only 30 to 50% of single cytologic smears obtained are read as positive for cancer hence, the use of pap smear alone for evaluation of suspicious lesion is discouraged. Importantly, these lesions should be directly biopsied."    ... Williams Gynae 1st /ed p 653
This means whenever a patient comes with specific complaint like post coital bleeding pap smear is not the initial test colposcopy should directly be done.
This rules out pap smear. Now read what Novaks has to say on this issue -
"When obvious tumor growth is present, a cervical biopsy is usually sufficient for diagnosis. If gross disease is not present, a colposcopic examination with cervical biopsies and endocervical curettage is warranted. If the diagnosis cannot be established conclusively with colposcopy and directed biopsies, cervical conization may be necessary."    ... Novak 14th /ed p 1405
Note: Colposcopy findings suggestive of invasive cancer cervix:


Abnormal blood vessels (abnormal reticular vessels)
Irregular surface contour with loss of surface epithelium.
Colour of the cervix changes from pink to yellowish orange.
Clinical examination and pap smear
Visual examination with lugol iodine
Visual examination with acetic acid
Colposcopy