Question

How do you verify `(1-cos2t)/ sin t= 2 sin t`?

Answer 1

use the fact that `cos2t=cos^2t-sin^2t` to get
`(1-cos^2t+sin^2t)/sint=2sint`
But `1=sin^2t+cos^2t`
So:
`(sin^2t+cancel(cos^2t)-cancel(cos^2t)+sin^2t)/sint=2sint`
`(2sin^cancel(2)t)/cancel(sint)=2sint`

`2sint=2sint`