How do you simplify the expression $1 - ({sec}^{2} x - {tan}^{2} x)$ $1-(sec^2x-tan^2x)$ ?

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How do you simplify the expression $1 - ({sec}^{2} x - {tan}^{2} x)$ $1-(sec^2x-tan^2x)$ ?

1 Answer

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Answer 1 · 2016-12-01T20:50:44

$0$ $0$

Explanation:

$1 - ({sec}^{2} x - {tan}^{2} x)$ $1-(sec^2x-tan^2x)$
$" "$
$= 1 - ({(\frac{1}{cos x})}^{2} - {(\frac{sin x}{cos x})}^{2})$ $=1-((1/cosx)^2-(sinx/cosx)^2)$
$" "$
$= 1 - (\frac{1}{{cos}^{2} x} - \frac{{sin}^{2} x}{{cos}^{2} x})$ $=1-(1/cos^2 x-sin^2 x/cos^2 x)$
$" "$
$= 1 - (\frac{1 - {sin}^{2} x}{{cos}^{2} x})$ $=1-((1-sin^2 x)/cos^2 x)$
$" "$
$= 1 - (\frac{{cos}^{2} x}{{cos}^{2} x})$ $=1-(cos^2 x/cos^2 x)$
$" "$
$= 1 - 1$ $=1-1$
$" "$
$= 0$ $=0$

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How do you simplify the expression $1 - ({sec}^{2} x - {tan}^{2} x)$ $1-(sec^2x-tan^2x)$ ?

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How do you simplify the expression 1−(sec2x−tan2x)1-(sec^2x-tan^2x)?

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Explanation:

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How do you simplify the expression $1 - ({sec}^{2} x - {tan}^{2} x)$ $1-(sec^2x-tan^2x)$ ?