Answering your question, I personally think that happiness can not exist without sadness since one complements the other, both are basic and infinite feelings in which a balance is necessary since the increase of one is the lack of the other.
That is something subjective that goes from the personal opinion of each person since some of the feelings automatically represent the feelings of the people in an eventual stage of time.
Happiness is the personal satisfaction of fulfilling some goal or goal of life, is to feel full with your life now, happy with your partner, happy with your work, but really before you get to that you must have gone through sadness, you must have had a bad experience in love to get to the point where you are today, or just a discussion with your current partner who got over and got where they are today ... you must have put papers in different jobs until you have one and have an interview, You must have gone through some moment of anguish or sadness before finding happiness and that is totally normal.
When we feel sad or discouraged, we come to think that life is cruel or unjust, so it is easy to understand why, in those moments, happiness seems to us the best goal of life or the "natural" state to achieve. However, that would overlook an important truth about human experience: sadness is an emotion as authentic as happiness. The moments of happiness and joy, and also the deeper sense of well-being that sometimes surrounds us, only make sense because they represent a sharp contrast to our experiences of disappointment, suffering and sadness, or even those moments when we feel trapped in a tedious routine.
For all this, sadness should never be repressed, nor any other feeling, but accept it, embrace it, welcome it into our lives, so that the things in our life are a kind of balance that allow us to flow.
Although without sadness there is no joy, always keep a happy perspective with you, try to have your willpower accompany you at all times, remember that although it is sometimes necessary to fall, even on your knees, to resume our life with a renewed impulse, You can discover happiness after a fall, however unexpected it may be.
And you, do you consider that without sadness there is no happiness or have another different point of view?