verify the identity cos(pi - theta) + sin(pi/2 + theta)=0

Question

anonymous · Answer

cot ( theta - pi / 2 )= cos ( theta - pi / 2 ) / sin ( theta - pi / 2 )

cos ( theta - pi / 2 )= cos(theta) cos (pi/2) + sin(theta) sin (pi/2)
                             = cos(theta) (0) + sin(theta) (1)
                             = sin(theta)

sin ( theta - pi / 2 )= sin(theta) cos(pi/2) - cos(theta) sin(pi/2)
                            = sin(theta) (0) - cos(theta) (1)
                            = -cos(theta)
so you get,
cot ( theta - pi / 2 )= sin(theta) /  -cos(theta)
cot ( theta - pi / 2 )= -tan(theta)

raden · Answer

use these identities 
cos(pi - x) = - cos(x)
sin(pi/2 + x) = cos(x)