How do you simplify $(1- tan^2θ) /( 1+ tan^2 θ)$ ?

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How do you simplify $(1- tan^2θ) /( 1+ tan^2 θ)$ ?

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Answer 1 · 2018-03-25T16:41:45

$2cos^2theta-1$ or $cos2theta$

Explanation:

Using the identities:
$1+tan^2theta= sec^2theta$
$1/sectheta= costheta$
$tantheta= sintheta/costheta$
$sin^2theta= 1-cos^2theta$
$2cos^2theta-1= cos2theta$

Start:
$(1-tan^2theta)/(1+tan^2theta)=$

$(1-tan^2theta)/(sec^2theta)=$

Split the numerator:

$1/sec^2theta-tan^2theta/sec^2theta=$

$cos^2theta-sin^2theta/cancel(cos^2theta)*cancel(cos^2theta)=$

$cos^2theta-(1-cos^2theta)=$

$2cos^2theta-1=$

$cos2theta$

Answer 2 · 2018-03-25T19:03:31

$cos2theta$

Explanation:

$"using the "color(blue)"trigonometric identities"$

$•color(white)(x)tantheta=sintheta/costheta$

$•color(white)(x)sin^2theta+cos^2theta=1$

$•color(white)(x)cos^2theta-sin^2theta=cos2theta$

$rArr(1-tan^2theta)/(1+tan^2theta)$

$=(1-sin^2theta/cos^2theta)/(1+sin^2theta/cos^2theta)xxcos^2theta/cos^2theta$

$=(cos^2theta-sin^2theta)/(cos^2theta+sin^2theta)$

$=cos^2theta-sin^2theta=cos2theta$

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How do you simplify $(1- tan^2θ) /( 1+ tan^2 θ)$ ?

2 Answers

Explanation:

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How do you simplify (1- tan^2θ) /( 1+ tan^2 θ)(1- tan^2θ) /( 1+ tan^2 θ)?

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Explanation:

Explanation:

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How do you simplify $(1- tan^2θ) /( 1+ tan^2 θ)$ ?