Verify the identity.

Question

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

Answer 1

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

 

Now cos(x - π/2) = cox(x)cos(π/2) + sin(x)sin(π/2)

                         = cos(x) * 0 + sin(x) * 1

                         = sin(x)

Also, sin(x - π/2) = sin(x)cos(π/2) - cos(x)sin(2)

                         = sin(x) * 0 - cos(x)*1

                         = -cos(X)

 

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

                 = sin(x)/(-cos(x))

                 = -(sin(X)/cos(x)) = -tan(x)