A fun activity to try with your Precalc/Alg2 class when they’re working on proving trig identities is to have them create their own trig identity.
Have them start with a true statement, then modify it by doing much of what you might ask them not to do during a trig proof (work across the equal sign). When they’ve made it properly obfuscated, have them write down the last line on a post it, erase their work and then ask them to prove their identity. If they can prove it then you can switch post-its with other students in the class to try and prove someone else’s “identity”.
Some students always get REALLY into this, and will probably not be able to finish before the block ends. Here’s a student plugging in his identity into desmos to verify that it’s true before he attempted to prove it.
These type of students often come back after a week having worked on some monstrosity of a proof. Honor them!