There are stupid people everywhere, unfortunately.
Also sadly except in unusual circumstances (e.g. they have a trust fund to live off), pre-calc teachers are not going to know much about mathematics.
Those trig identities were tremendously useful throughout Calculus. Having them readily accessible in memory was very helpful, from what I recall. Why do you think this pre-calc teacher was “stupid”?
I'm not sure what you mean by "real" calculus course. Physics applies calculus to solve certain problems. To claim one subject is more "real" than the other doesn't make sense to me.
