Question

Verify the identity. Show your work.

cot θ ∙ sec θ = csc θ

Answer 1

What are the cot and sec identities in terms of sin and cos?
Substitute cot and sec on the left side using those identities.

Answer 2

i need help like step by step because I don't get it

Answer 3

The sine and cosine are simple trig functions.
The other 4 trig functions can be written in terms of the sine and cosine like this:

\(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\)

\(\cot \theta = \dfrac{\cos \theta}{\sin \theta}\)

\(\sec \theta = \dfrac{1}{\cos \theta}\)

\(\csc \theta = \dfrac{1}{\sin \theta}\)

Answer 4

Do you understand so far?

Answer 5

Now look at the left side of the identity you want to prove.
There is a cotangent and a secant.
Using the 4 identities above that I gave you, replace both the cotangent and the secant by what they are equal to. Then simplify the left side. Then use another identity of the 4 above to prove the left side is equal to the right side.