What is the relationship defined by the Pythagorean identity for cosecant and cotangent?

The Pythagorean identity that relates cosecant and cotangent is correctly expressed as csc²(θ) - cot²(θ) = 1. This relation is derived from the fundamental Pythagorean identity in trigonometry, which states that sin²(θ) + cos²(θ) = 1.

Cosecant and cotangent are defined in terms of sine and cosine as follows:

• Cosecant is the reciprocal of sine, csc(θ) = 1/sin(θ).

• Cotangent is the quotient of cosine and sine, cot(θ) = cos(θ)/sin(θ).

When you square both cosecant and cotangent, you obtain:

csc²(θ) = 1/sin²(θ) and cot²(θ) = cos²(θ)/sin²(θ).

Substituting these into the identity gives:

1/sin²(θ) - cos²(θ)/sin²(θ) = 1.

Combining terms yields:

(1 - cos²(θ))/sin²(θ) = 1.

Using the identity 1 - cos²(θ) = sin²(θ) leads