Trigonometric Identities|Please help!

Question

Please help me understand how to verify the trigonometric identity:

cot²θ

⎯⎯ * sec²θ = 7tanθ cosθ csc²θ

csc θ

Answer 1

I would suggest checking if there's actually supposed to be a "7" on the right-hand side. If you drop that "7," the identity does work out. You can see this by following the previous expert answer and omitting the "7."

Answer 2

Rewrite all the terms in terms of sin and cos:

cotθ = cosθ / sinθ

cscθ = 1 / sinθ

secθ = 1 / cosθ

tanθ = sinθ / cosθ

Left-hand side turns into:

((cos²θ / sin²θ) / (1 / sinθ)) * (1 / cos²θ)

Which simplifies to:

1 / sinθ

Right-hand side turns into:

7 * (sinθ / cosθ) * cosθ * (1 / sin²θ)

Which simplifies to:

7 / sinθ

Since the left-hand side and the right-hand side do not equal each other, we have verified that the identity does not hold.

Hope this was helpful.