This question requires the understanding of trigonometric identities. I'll list the ones that are needed to answer this question:
cotθ = 1 / tanθ
tanθ = sinθ / cosθ
Look at the latter identity. We can rewrite it as such:
tanθ * cosθ = sinθ
We are given the expression:
cosθ * tan²θ * cotθ
Referring to the first trigonometric identity above, substitute cotθ:
cosθ * tan²θ * (1 / tanθ)
Multiply tan²θ and the fraction:
cosθ * (tan²θ / tanθ)
cosθ * tanθ
Refer to the second trigonometric identity:
cosθ * tanθ
sinθ
cosθ * tan²θ * cotθ = sinθ
If you have any questions about how I got to the answer, feel free to ask
- breezyツ
