Question

Using trigonometric identities to simplify the following expression:
tan(θ)cot(θ)

Answer 1

Explanation:

The expression tan(θ)cot(θ) can be simplified using the trigonometric identity:

tan(θ) = sin(θ) / cos(θ)

cot(θ) = cos(θ) / sin(θ)

So,

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

= sin(θ) x cos(θ) / (cos(θ) x sin(θ))

= sin^2(θ) / sin^2(θ)

= 1

Therefore, tan(θ)cot(θ) = 1.