Can you solve $\int \sin(t)^2\, dt$ without trigonometric identities?
I wanted to solve this integral and I actually had a rough time with it... First I tried a normal product integration, with $u'=\sin(t)$ and $v=\sin(t)$, which lead nowhere.
Then I tried $u'=1$ and $v=\sin(t)^2$ which was actually do able, with the identity $\sin(t)\cos(t)=2\sin(2t)$, which I had to look up...
But the easiest way seems to be, that one uses $\sin(t)^2=\frac12-\frac12\cos(2t)$
The problem is, that you have to know these identities. Which I barely do.
Is there an elementary way to solve this integral, which uses as less knowledge about these identities as possible.