How do you simplify the expression $(sec x - 1) (sec x + 1)$ $(secx-1)(secx+1)$ ?

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Answer 1 · 2016-08-21T09:05:52

${tan}^{2} x$ $tan^2x$

$(sec x - 1) (sec x + 1) = {sec}^{2} x - 1$ $(sec x-1)(sec x +1) =sec^2 x-1$

The one trig identity to remember is

${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x +cos^2x =1$

Divide through by ${cos}^{2} x$ $cos^2x$ to give

${tan}^{2} x + 1 = {sec}^{2} x$ $tan^2x + 1 = sec^2x$

Rearrange

And you have your answer

How do you simplify the expression (secx−1)(secx+1)(secx-1)(secx+1)?