Both of these hairy issues are related to excess androgens that are part of PCOS. Our hair follicles respond overzealously to testosterone creating both hair loss and hair growth. This is because the follicles on the face tend to stretch and grow causing the hair to get stuck and not fall out when they should. Conversely, the scalp hair follicles actually shrink in response to androgens and the hair can fall out or just not be as robust.
The first step in treatment is to identify the cause of the hair loss. Then, treat it appropriately. If an internal cause is the culprit, it should be addressed — for example, thyroid medication for thyroid disease or supplements for a nutritional deficiency. External skin conditions are often treated with topical medications, and, once treated, the hair loss usually recovers. I often recommend Latisse as an adjunctive treatment. Though frequently associated with eyelash lengthening, it is a great option for thickening brows. In fact, people with brows that thin with aging (I typically don't see this in women under 50) may want to opt for Latisse.
Thyroid hormone receptors were detected in both dermal and epithelial compartments of the human pilosebaceous unit. T4 and T3 decrease the apoptosis of hair follicles and T4 prolongs the duration of anagen in vitro. Thyroidectomy delays initiation of anagen. Administration of thyroxine advances anagen, initiation of which is however delayed once toxic doses are given. Therefore, ratio of telogen to anagen hairs is increased in hypothyroidism as well as hyperthyroidism. Thus, the hair follicles are affected in thyroid disorders, and madarosis is caused due to disturbances in hair cell kinetics. Hypothyroidism is associated with generalized hair loss probably due to coarse, dull, and brittle hair with reduced diameter. The eyebrows and eyelashes may also be lost. Loss of lateral one-third of eyebrows known as Hertoghe sign is a characteristic sign of hypothyroidism. Some people also refer to it as Queen Anne's sign, after Anne of Denmark whose portrait with shortened eyebrows has been interpreted by some as indicative of the presence of goiter, even though such a fact has not been proved by any known sources of information. Madarosis may even be the presenting sign in hyperthyroidism. In hyperthyroidism, there is thinning with breaking off and shortening of hair. Madarosis can also occur in hypopituitarism, hypoparathyroidism, and hyperparathyroidism.