How do you perform addition or subtraction and use the fundamental identities to simplify $\frac{1}{sec x + 1} - \frac{1}{sec x - 1}$ $1/(secx+1)-1/(secx-1)$ ?

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Answer 1 · 2017-02-11T18:30:15

$\frac{1}{sec x + 1} - \frac{1}{sec x - 1} = - 2 {cot}^{2} x$ $1/(secx+1)-1/(secx-1)=-2cot^2x$

$\frac{1}{sec x + 1} - \frac{1}{sec x - 1}$ $1/(secx+1)-1/(secx-1)$

= $\frac{sec x - 1 - sec x - 1}{{sec}^{2} x - 1}$ $(secx-1-secx-1)/(sec^2x-1)$

= $- \frac{2}{{tan}^{2} x}$ $-2/tan^2x$

= $- 2 {cot}^{2} x$ $-2cot^2x$

How do you perform addition or subtraction and use the fundamental identities to simplify 1secx+1−1secx−11/(secx+1)-1/(secx-1)?