- #1
Jen23
- 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