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

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Answer 1 · 2016-07-08T07:59:51

$2cot^2x$

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

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

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

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

$=2/tan^2x=2cot^2x$

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