School daze

I remember one day in coaching class, our maths teacher walked in, wrote all these trigonometric identities on the board, told us he would be back in 15 minutes, and we were to memorize all of these by that time. I remember the general groaning that followed this announcement, because we knew he wasn't kidding.

sin(A + B) = sin A cos B + cos A sin B

sin(A - B) = sin A cos B - cos A sin B

cos(A + B) = cos A cos B - sin A sin B

cos(A - B) = cos A cos B + sin A sin B

tan(A + B) = [ tan A + tan B ] / [ 1 - tan A tan B]

tan(A - B) = [ tan A - tan B ] / [ 1 + tan A tan B]

sin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2 ]

sin A - sin B = 2 cos [ (A + B) / 2 ] sin [ (A - B) / 2 ]

cos A + cos B = 2 cos [ (A + B) / 2 ] cos [ (A - B) / 2 ]

cos A - cos B = - 2 sin [ (A + B) / 2 ] sin [ (A - B) / 2 ]

2 sin A cos B = sin (A + B) + sin (A - B)

2 cos A sin B = sin (A + B) - sin (A - B)

2 cos A cos B = cos (A + B) + cos (A - B)

2 sin A sin B = - cos (A + B) + cos (A - B)

sin 2A = 2 sin A cos A

cos 2A = cos ² A - sin ² A = 2 cos ² A - 1 = 1 - 2 sin ² A 

sin 3A = 3 sin A - 4 sin ³ A

cos 3A =  4 cos ³ A - 3 cos A

He came back in half an hour. We had tried our best, but of course there was no way we could memorise so many formulae the first time we'd seen them. He erased the board and then started asking one by one. If you couldn't answer correctly, you remained standing, while the next person in the row tried their best to remember what the answer was. I think by the end of that hour, most of the class was standing.

But I still remember those formulae. I still remember that the expansion of cos(A+B) has a negative sign in its expansion, and the last of the sin-cos combinations, sinAsinB has a negative sign in front. So I guess I owe him for that.

I miss the days when I used to enjoy Maths, when I loved the challenge of solving a new question, as quickly as I could.