Question

Найдите значение выражения:
$1)4 \sin22 {}^{0} 30 {}^{'} \cdot \cos22 {}^{0} 30' \\ 2) \sqrt{2}( \cos {}^{2} 22.5 {}^{0} - \sin {}^{2} 22.5 {}^{0} )$
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Answer 1

$\displaystyle\bf\\1)\\\\2\cdot \underbrace{2Sin22^\circ30'\cdot Cos22^\circ30'}_{Sin(2\cdot 22^\circ30')}=2Sin45^\circ=2\cdot\frac{\sqrt{2} }{2}=\sqrt{2}\\\\\\2)\\\\\sqrt{2}\underbrace{(Cos^{2} 22,5^\circ-Sin^{2} 22,5^\circ)}_{Cos(2\cdot22,5^\circ) }=\sqrt{2} \cdot Cos45^\circ=\sqrt{2} \cdot\frac{1}{\sqrt{2} } =1$