Question

Помогите прошу 4cos15/√2(√3+1) 

Answer 1

$cos^2 x=\frac{1+cos(2x)}{2}$
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$sin^2 x=\frac{1-cos(2x)}{2}$
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$0^o$ $cos 15^o>0$
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$4cos15^o=4\sqrt{\frac{1+cos30^0}{2}}=\\\\4\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}=\\\\4*\sqrt{\frac{2+\sqrt{3}}{4}}=\\\\2\sqrt{\frac{4+2\sqrt{3}}{2}}=\\\\\sqrt{2}*\sqrt{3+2\sqrt{3}+1}=\\\\\sqrt{2}*\sqrt{(\sqrt{3})^2+2*\sqrt{3}*1+1^2}=\\\\\sqrt{2}*(\sqrt{3}+1)$
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$\frac{4cos15^o}{\sqrt{2}(\sqrt{3}+1)}=1$