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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$0^o<15^o<90^o$ $cos 15^o>0$
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$4cos15^o=4sqrt{frac{1+cos30^0}{2}}=\\4sqrt{frac{1+frac{sqrt{3}}{2}}{2}}=\\4*sqrt{frac{2+sqrt{3}}{4}}=\\2sqrt{frac{4+2sqrt{3}}{2}}=\\sqrt{2}*sqrt{3+2sqrt{3}+1}=\\sqrt{2}*sqrt{(sqrt{3})^2+2*sqrt{3}*1+1^2}=\\sqrt{2}*(sqrt{3}+1)$
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$frac{4cos15^o}{sqrt{2}(sqrt{3}+1)}=1$