Question

Verify the identity.
cot ( theta - pi / 2 ) = - tan theta

Answer 1

cot(theta -pi/2) = cos(theta - pi/2)/sin(theta - pi/2)
using cosine and sin law
= [cos(theta)*cos(pi/2)+sin(theta)*sin(pi/2)] / [sin(theta)*cos(pi/2) - cos(theta) * sin(pi/2)]
by simplify it :
= sin(theta) / -cos(theta)
= -tan(theta)