Question

How do you simplify `(cotx/cscx)^2+1/csc^2x`?

Answer 1

`(cotx/cscx)^2+1/csc^2x -= 1`

Explanation:

`cotx=1/tanx`; `cscx=1/sinx`; so:

`(cotx/cscx)^2+1/csc^2x = ((1/tanx)/(1/sinx))^2 + 1/(1/sin^2x)`
`= (sinx/tanx)^2+sin^2x`
`= sin^2x (1/tan^2x+1)`
`= sin^2x (cot^2x+1)`
`= sin^2x (csc^2x)`
`= sin^2x (1/sin^2x)`
`= 1`