"How to identify (sec⁡x−tan⁡x)2?" solved and explained

Draven Crane

Answered question

2023-01-21

How to identify

{(\sec x - \tan x)}^{2}

dejalacorrer9kv

Beginner2023-01-22Added 7 answers

We need

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

\sec x = \frac{1}{\cos x}

\tan x = \frac{\sin x}{\cos x}

a^{2} - b^{2} = (a + b) (a - b)

Hence,

{(\sec x - \tan x)}^{2}

= {(\frac{1}{\cos x} - \frac{\sin x}{\cos x})}^{2}

= \frac{{(1 - \sin x)}^{2}}{\cos^{2} x}

= \frac{{(1 - \sin x)}^{2}}{1 - \sin^{2} x}

= \frac{{(1 - \sin x)}^{2}}{(1 + \sin x) (1 - \sin x)}

= \frac{1 - \sin x}{1 + \sin x}

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