Step 1: The pituitary gonadotropins FSH and LH are controlled by negative feedback from the ovarian hormones. The key is to find the hormone that suppresses both gonadotropins.
Step 2: Estrogen is secreted in response to both LH and FSH stimulation, and through negative feedback it in turn inhibits both LH and FSH. It acts at both the hypothalamus and the pituitary, making it the one hormone that suppresses both gonadotropins.
Step 3: Comparing the more selective feedback signals: progesterone mainly inhibits LH, while inhibin (from granulosa cells) selectively inhibits FSH and acts only at the pituitary. So progesterone does not suppress both, which is why option d is not the best answer.
Step 4: Cortisol and aldosterone are adrenal corticosteroids and are not the physiological feedback regulators of FSH and LH, so options a and b are wrong. The hormone that inhibits both gonadotropins is estrogen, option c. (Note: at the mid-cycle peak, sustained high estrogen switches to positive feedback to trigger the LH surge.)