Question
Simplify cot(90 degrees-theta/cot theta
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GPT 3.5
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).
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).