Question

How do you simplify `cos x /( sec x -1) + cos x / (sec x +1)`?

Answer 1

`2cot^2x`

Explanation:

`cosx/(secx-1)+ cosx/(secx+1)`

`=cosx(1/(secx-1)+ 1/(secx+1))`

`=cosx((secx+1+secx-1)/((secx-1)(secx+1)))`

`=(cosx*2secx)/(sec^2x-1)`

`=2/tan^2x=2cot^2x`