Mathematics

Problem

Starting with the identity

1+\tan^2 x = \sec^2 x

, a student performs the following two steps: (i) divides both sides by

\tan^2 x

, (ii) replaces

\dfrac{1}{\tan x}

with

\cot x

. Which of the following identities should the student obtain? a)

\cot^2 x - 1 = \csc^2 x

\cot^2 x + 1 = \sec^2 x

1+\cot^2 x = \csc^2 x

1+\cot^2 x = \csc x