Answered: "How to simplify the expression 1−sec2x?"

stampedazt0

Answered question

2022-12-27

How to simplify the expression

1 - \sec^{2} x

Marco Ochoa

Beginner2022-12-28Added 8 answers

Begin from the

b a s i c t r i g o n o m e t r i c i d e n t i t y

∣ \overset{―}{\underset{―}{\frac{a}{a} \sin^{2} x + \cos^{2} x = 1 \frac{a}{a} ∣}}

divide all terms on both sides by

\cos^{2} x

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

R e min d e r

∣ \overset{―}{\underset{―}{\frac{a}{a} \tan x = \frac{\sin x}{\cos x} and \sec x = \frac{1}{\cos x} \frac{a}{a} ∣}}

Therefore, identity becomes simpler.

\tan^{2} x + 1 = \sec^{2} x \Rightarrow \tan^{2} x = \sec^{2} x - 1

multiply through by -1

\Rightarrow - \tan^{2} x = 1 - \sec^{2} x

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