I’m one who really hates memorizing formulas, be in as a student or tutor. So I shall share how I remember the three very useful trigonometry identities. I’ll start with the one which you all definitely can identify with.

$sin^{2}x + cos^{2}x = 1$

### Now how do we get the other 2?

Simply divide the above equation by $sin^{2}x$ and $cos^{2}x$ respectively.
Lets divide by $sin^{2}x$!
$\frac{sin^{2}x}{sin^{2}x} + \frac{cos^{2}x}{sin^{2}x} = \frac{1}{sin^{2}x}$
Voila! we have $1 + cot^{2}x = cosec^{2}x$

You can try to do the same with $cos^{2}x$! Let me know if you have problems!