How do you identify $(secx-tanx)^2$ ?

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Answer 1 · 2017-05-04T13:27:09

The answer is $=(1-sinx)/(1+sinx)$

We need

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

$secx=1/cosx$

$tanx=sinx/cosx$

$a^2-b^2=(a+b)(a-b)$

Therefore,

$(secx -tanx)^2$

$=(1/cosx-sinx/cosx)^2$

$=(1-sinx)^2/cos^2x$

$=(1-sinx)^2/(1-sin^2x)$

$=(1-sinx)^2/((1+sinx)(1-sinx))$

$=(1-sinx)/(1+sinx)$

How do you identify (secx-tanx)^2(secx-tanx)^2?