I'm currently studying aerodynamics. I have realized that a sudden encounter with a headwind during descent will result in the aircraft generating more lift, thus angle of descent decreases. I haven't studied the descent in a constant headwind, but through research I've come across that a constant headwind during descent will increase the angle of descent. This does not make sense. Shouldn't the angle of descent decrease in both situations? Will appreciate it if someone could explain this.
You have to consider the difference between rate of descent and angle of descent.
The rate of descent is expressed in distance/time, usually feet/second. This is determined by your airspeed and trim configuration. The ground speed does not affect this, only airspeed.
The angle of descent is the angle the plane is flying with respect to the ground.
When flying into a steady headwind the ground speed will be lower at the same airspeed. But the descent rate will be the same. So if you're descending at the same rate, but moving forward at a slower rate then the angle will be steeper.
On the other hand, a transient gust of wind will temporarily increase the airspeed. When the gust hits it will take a moment to overcome the inertia and slow the aircraft. So momentarily your airspeed will increase but your ground speed stay the same. An increase in airspeed will mean more lift, thus a lower descent rate at the same forward ground speed. A lower descent rate at the same ground speed will yield a shallower angle.
Consider descending in zero wind, trimmed to an airspeed of 80m/s (288km/h) and a sink rate of 2m/s. You won't touch stick, trim tabs or throttles during the descent, but you will encounter a headwind at a later time. For now, ground speed is equal to airspeed and the angle of descent is 1:40.
You suddenly encounter a headwind of 20m/s. Ground speed remains at 80m/s due to inertia; Airspeed rises to 100m/s. The rise in airspeed increases lift and reduces sink rate to 1m/s. The angle of descent is now much shallower, at 1:80.
After a couple of seconds, airspeed bleeds off and the aircraft resumes its trimmed state at an airspeed of 80m/s and a sink rate of 2m/s. This time, the ground speed is only 60m/s due to the headwind and the angle of descent is now 1:30.