- #1

- 12

- 0

## Homework Statement

Express (1+cot^2 x) / (cot^2 x) in terms of sinx and/or cosx

## Homework Equations

cot(x) = 1/tan(x)

sin^2(x) + cos^2(x) = 1

## The Attempt at a Solution

I do not know if I am solving this problem correctly. Is there an easier route than the way I have solved it, if it is solved correctly?

= (1+cot^2x) / (cot^2x)

= 1+ [ (cos^2x) / (sin^2x) ] ÷ [ (cos^2x) / (sin^2x) ]

= 1 + [ (cos^2x) / (sin^2x) ] x [ (sin^2x / cos^2x) ]

= [ (sin^2x / sin^2x) + (cos^2x / sin^2x) ] x [ (sin^2x) / (cos^2x) ]

= [ (sin^2x + cos^2x) / (sin^2x) ] x [ (sin^2x )/ (cos^2x) ]

= [ 1 / sin^2x ] x [ sin^2x / cos^2x]

= sin^2x / (sin^2x)(cos^2x)

= 1 / cos^2x