How do you simplify $cos 2 x = \frac{1 - {tan}^{2} x}{1 + {tan}^{2} x}$ $cos 2x = (1-tan^2x)/(1+tan^2x)$ ?

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How do you simplify $cos 2 x = \frac{1 - {tan}^{2} x}{1 + {tan}^{2} x}$ $cos 2x = (1-tan^2x)/(1+tan^2x)$ ?

1 Answer

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Answer 1 · 2018-03-25T13:01:49

Kindly go through a Proof in the Explanation.

Explanation:

We have, $cos 2 x = {cos}^{2} x - {sin}^{2} x = \frac{{cos}^{2} x - {sin}^{2} x}{1}$ $cos2x=cos^2x-sin^2x=(cos^2x-sin^2x)/1$ ,

$= \frac{{cos}^{2} x - {sin}^{2} x}{{cos}^{2} x + {sin}^{2} x}$ $=(cos^2x-sin^2x)/(cos^2x+sin^2x)$ ,

$= \frac{{cos}^{2} x {1 - \frac{{sin}^{2} x}{{cos}^{2} x}}}{{cos}^{2} x {1 + \frac{{sin}^{2} x}{{cos}^{2} x}}}$ $=[cos^2x{1-sin^2x/cos^2x}]/[cos^2x{1+sin^2x/cos^2x}]$ .

$\Rightarrow cos 2 x = \frac{1 - {tan}^{2} x}{1 + {tan}^{2} x}$ $rArr cos2x=(1-tan^2x)/(1+tan^2x)$ , as desired!

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How do you simplify $cos 2 x = \frac{1 - {tan}^{2} x}{1 + {tan}^{2} x}$ $cos 2x = (1-tan^2x)/(1+tan^2x)$ ?

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Explanation:

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How do you simplify cos2x=1−tan2x1+tan2xcos 2x = (1-tan^2x)/(1+tan^2x)?

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Explanation:

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How do you simplify $cos 2 x = \frac{1 - {tan}^{2} x}{1 + {tan}^{2} x}$ $cos 2x = (1-tan^2x)/(1+tan^2x)$ ?