Question

lg(2cos15) / lg(2sin15)

Answer 1

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Answer 2

$frac{lg(2cos15)}{lg(2sin15)} =frac{lg(2*sqrt{frac{1+cos30}{2}})}{lg(2*sqrt{frac{1-cos30}{2}})} =frac{lg(sqrt{2+2cos30})}{lg(sqrt{2-2cos30})} =frac{lg(sqrt{2+sqrt{3}})}{lg(sqrt{2-sqrt{3}})} =frac{lg(2+sqrt{3})^{0.5}}{lg(2-sqrt{3})^{0.5}} =\ \ = frac{0.5lg(2+sqrt{3})}{0.5lg(2-sqrt{3})} =frac{lg(2+sqrt{3})}{lg(2-sqrt{3})} =frac{lgfrac{(2+sqrt{3})(2-sqrt{3})}{2-sqrt{3}}}{lg(2-sqrt{3})}=frac{lgfrac{4-3}{2-sqrt{3}}}{lg(2-sqrt{3})}=$

$=frac{lgfrac{1}{2-sqrt{3}}}{lg(2-sqrt{3})}=frac{lg(2-sqrt{3})^{-1}}{lg(2-sqrt{3})} =frac{-lg(2-sqrt{3})}{lg(2-sqrt{3})} =-1 \ \ OTBET: -1$