Question

Prove formula
* cos 2x =1-tan2x/1+tan2x

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Answer 1

$\huge \bf \underline \red{Answer}$

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$\sf \huge \underline{Question}$

$\rm{ \cos(2x) = \frac{1 - {tan}^{2}x }{1 + {tan}^{2} x}}$

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step by step explanation:

$\tt{cos \: 2x = \frac{1 - {tan}^{2}x }{1 + {tan}^{2} x}}$

$\tt{cos \: 2x = {cos}^{2}x - {sin}^{2}x = { {cos}^{2}x - {sin}^{2}x }^{1}}$

$\tt \red{⟹ \: = \frac{ {cox}^{2}x - {sin}^{2} x}{ {cos}^{2}x + {sin}^{2} x} }$

$\tt \blue{⟹ \: \frac{ {cos}^{2} x \: 1 - \frac{ {sin}^{2}x }{ {cos}^{2}x } }{ {cos}^{2} x \: 1 + \frac{ {sin}^{2}x }{ {cos}^{2} x}</u><u>}</u><u> }$

$\tt \pink{⟹cos \: 2x = \frac{1 - {tan}^{2}x }{1 + {tan}^{2} x}}$

I hope its help uh