"If I add sin(x) to both sides of the equation, then I can use such-and-such identity which makes this equal foo."
If you don't make the correct mental leap, then you get completely stuck and it's really easy to give up.
* enough memory to remember the identities * fast enough recall of identities from memory @ * fast enough exploration of possible solutions @
@ Fast enough is when you can do it all within the amount of time it takes for solving the problem to give enjoyment rather then ending a frustration.
Without the above I have to use different, usually more intentional, strategies.
"If I add sin(x) to both sides of the equation, then I can use such-and-such identity which makes this equal foo."
If you don't make the correct mental leap, then you get completely stuck and it's really easy to give up.