Question

Use the fundamental identities to simplify the expression:

cot beta sec beta

I used 1+tan^2u=secu since cot is the inverse of tan. I flipped the tangent, then so it was 1+ (1/tan). But the book's answer is the cosecant of beta. Where did this come from??

Answer 1

Fundamental identities include:
cot(β)=cos(β)/sin(β)
sec(β)=1/cos(β), and
csc(β)=1/sin(β)

I will let you take it from here.

Answer 2

Is the right answer 1/sinB?

Answer 3

That's correct, although 1/sin(β) is generally written as csc(β), as your answer indicates.