Is there really a secret for singing in the high range?
Physiologically, to sing high is just to stretch your vocal cords and keep them connected at the same time, all the while applying the right amount of pressure from the support system. This means your laryngeal mechanism has to obey the orders of your brain: sing higher. What happens? The thyroid cartilage tilts so that the vocal folds can become longer and thinner, vibrating only by their edges,  thus stretching and creating a higher  pitch. It is really quite simple – the actual physical micro mechanism needn´t be explained any further for us to comprehend what is going on. Subjectively, this means we must give the larynx every possible opportunity to “do its thing” – to let it function naturally. But what does that mean in practice? Why do we often hinder this natural mechanism from taking place?
The larynx naturally wants to rise when singing higher pitches. This, while being natural, on the other hand, makes the sound often shrill and strained, not so desirable qualities. For the vocal folds to stretch according to pitch (which happens quite automatically) there really only needs to be freedom and relaxation, but what usually happens is tightening and closing of the vocal tract, that is the throat. To make things worse, we usually try to compensate by adding more pressure (usually thinking we are supporting better).  For classical singing, there is an ideal of keeping the larynx relatively low while attempting to sing high which really is quite unnatural physiologically! But there is a way: to sing high and keep the larynx lower, you must find a special balance, thus creating this characteristic sound required of a classical singer. It is really a phenomenon of the past 200 years, since the development of bel canto towards the more dramatic vocal expression of the Romantic and Wagnerian singing ideal. Even today, we want to hear a voice to sound chiaroscuro, the Italian equivalent of dark and bright at the same time. This can be technically realized by keeping the larynx relatively low (not as low as possible!) while at the same time activating the higher and brighter harmonics and overtones of the masque, the resonating cavities high in the head. It is not easy! This is vocal art, a highly developed skill.
Singing teachers have a large variety of ways to achieve this ideal. To keep the larynx low while singing high, they often stress the importance of the breathing mechanism, the low support. If the diaphragm is retarded in its ascent after inhalation, this naturally keeps the larynx lower (the so called diaphragmatic support and the  tracheal pull, research by Sundberg).   Modifying the vowels is another way, applied together with the previous system. It involves the use of the pharynx which is the main resonator of all our cavities. To achieve the maximum use of the pharynx we must also find the best open position of the jaw. Many singers have great problems opening the jaw, tensions, either pulling it back or pushing it forward, or generally just not opening enough for good quality of high notes. You really have to find your best way, individually, because the jaw opening is not the same for everyone but it is nevertheless of great importance.  Our physical structures differ considerably in size . A large jaw is usually an asset for a singer (look at Joan Sutherland!). Those with more fragile facial structures will have to work out the opening just suitable for them.
Thus, singing high notes really is an art, answering the needs and wishes of the international audience who wants to hear nice, round, clear and velvety high notes that still carry well. Not an easy task!
But quite a different ideal arises for the singer in musical theatre singing with a microphone.  The high notes are no longer dependent on the singer´s ability to project acoustically, but instead it is required that the  high range  express emotion as naturally as possible, without shouting. You need a special technique, either belting or the so called legit. This way of singing really is quite different from classical technique, in that it does not require a lowered larynx. Still you must be able to stretch the cords without straining, the larynx must be in a higher position while maintaining the open throat. The twang or the use of the epiglottic funnel can be used for carrying power and to help the stretch.  When correctly applied, it does no harm to the vocal mechanism but it has to be learned just as thoroughly as any vocal technique.