Verify the identity. justify each step.

From the trigonometry:

tan θ = (sin θ) / (cos θ)
cot θ = (cos θ) / (sin θ)

∴ tan θ + cot θ = (sin θ) / (cos θ)  +  (cos θ) / (sin θ)
  = [ sin² θ + cos² θ]/( sin θ cos θ) = 1 /( sin θ cos θ )

note :   sin² θ + cos² θ = 1