Can someone walk me through simplifying sec(?)?^2 * cot(?) * cos(?) =

Question

 

I thought it'd be  (1 / cos(θ)²) * (1 / tan(θ)) * (cos(θ) / 1)

 

Which would get you cos(θ) / cos(θ)2 * tan(θ)

 

And then coming out to 1 / cos(θ) * tan(θ)

 

but that doesn't make sense cuz these are the multiple choice answers given.

 

 

 

(A) sec θ (B) csc θ (C) sin θ (D) cos θ (E) cot θ

 

 

 

EDIT: So I just realized that cot(θ) can be cos(θ) / sin(θ)

 

So after redoing the problem I get cos(θ)² / cos(θ)2 * sin(θ)

 

Which simplifies out to 1 / sin(θ)  which equals csc(θ)      Can someone confirm this?

Answer 1

sec²θcotθcosθ =(1/cos²θ)(cosθ/sinθ)(cosθ) = 1/sinθ = cscθ...choice B.