Respuesta :

tanθ + cotθ = 1/sinθcosθ

since we know that;

tanθ = sinθ/cosθ, and

cotθ = cosθ/sinθ

now when we add tanθ and cotθ and replace their values;

tanθ + cotθ=sinθ/cosθ + cosθ/sinθ

For a common denominator to add those two fractions, the obvious choice is sinθ.cosθ , so

tanθ + cotθ = sin²θ/sinθcosθ + cos²θ/sinθcosθ =sin²θ + cos²θ / sinθcosθ

now we can use the identity that;

sin²θ + cos²θ = 1

So,

tanθ + cotθ = 1/sinθcosθ