Simplify cot(90 degrees-theta/cot theta

Answer 1

We can simplify cot(90 degrees - θ) / cot(θ) using trigonometric identities.

First, let's write 90 degrees as π/2 radians.

cot(90 degrees - θ) / cot(θ) = cot(π/2 - θ) / cot(θ)

Now, we can use the identity cot(π/2 - θ) = tan(θ).

cot(π/2 - θ) / cot(θ) = tan(θ) / cot(θ)

Since cot(θ) = 1/tan(θ), we can rewrite the expression as:

tan(θ) / (1/tan(θ))

Multiplying the numerator and denominator by tan(θ), we get:

tan^2(θ) / 1

Therefore, cot(90 degrees - θ) / cot(θ) simplifies to tan^2(θ).