Question

Help Please:

Answer 1

@imqwerty @sweetburger

Answer 2

cot (x - pi/2) = cos( x-pi/2) / sin(x - pi/2)

cos(a-b) = cos(a)cos(b) +sin(a)sin(b)
cos(x-pi/2) = cos(x) cos(pi/2) + sin(x) sin(pi/2)
cos(x-pi/2) = cos(x) (0) + sin(x) (1) = sin (x)

sin(a-b) = sin(a)cos(b) -cos(a)sin(b)
sin(x-pi/2) = sin(x) cos(pi/2) - cos(x) sin(pi/2)
sin(x-pi/2) = sin(x) (0) = -cos(x) (1)

cos(x-pi/2) / sin(x-pi/2) = sin(x) / [-cos(x)] = -tan(x)

Answer 3

There is an easier way but that is probably the one that you are looking for.

Answer 4

Yes, are you aware of the double angle formula?\[\large\rm tan(\alpha+\beta)= \frac{tan(\alpha)+tan(\beta )}{1-tan(\alpha)tan(\beta )}\]

Answer 5

thank you both! yes, I'm aware