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Mathematics, 07.09.2021 14:00 honestty21

Plz help me solve this $State\: factor \: therom$

$if \: \sin(a) = \frac{3}{5} \: find \: the \: value \: of \: \cos(2a)$
$prove \: that \frac{2 \tan((45 - \alpha ) }{2 + \tan(45 - \alpha )} = \cos( 2\alpha )$
$solve \: {x}^{3} - 19x - 30 = 0$
$prove \: that \: \sqrt{2 + \sqrt{2 + \sqrt{2 + 2 \cos(8a) } } } = 2 \cos(a)$
$\frac{ \sqrt{3} }{ \sin(20) } - \frac{1}{ \cos(20) } = 4$

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