Question

Verify the identity.

cot(x-pi/2) = -tan x

Answer 1

cot (x - Pi/2) = cos (x- Pi/2)/sin (x - Pi/2)
Use the trig identities: cos (a - b) = cos a*cos b- sin a*sin b
sin (a - b) = sin a*cos b -sin b*cos a
cos (x - Pi/2) = - sin x, because cos Pi/2 = 0, and sin Pi/2 = 1
sin (x - Pi/2) = cos x, because cos b = 0, and sin b = 1
Finally: cot (x - Pi/2) = -sin x/cos x = tan x.