Question

Verify the identity. Show your work.


cot θ ∙ sec θ = csc θ

Answer 1

cotθ=1/tanθ=1/(sinθ/cosθ)=cosθ/sinθ <--- trig identity
secθ=1/cosθ <--- trig identity
cotθ*secθ=(cosθ/sinθ)*(1/cosθ)
cosθ/(sinθcosθ) <--- combine denominators
1/sinθ <--- cancel out the cosθ
csc=1/sinθ <--- trig identity
∴cotθ*secθ=cscθ

Answer 2

Therefore, Verify.

Explanation:

Given : cot θ ∙ sec θ = csc θ

To find : Verify the identity.

Solution : We have given

cot θ ∙ sec θ = csc θ

By the trigonometric identity : cot θ =
`(cos(theta))/(sin(theta))` .

sec θ =
`(1)/(cos(theta))`.

Then ,

Taking left hand side

cot θ ∙ sec θ

`(cos(theta))/(sin(theta))` *
`(1)/(cos(theta))`

`(1)/(sin(theta))`

csc θ = right hand side.

Hence verify.

Therefore, Verify.