Question

Решите пожалуйста пример

Answer 1

sin7гр15мин=$sqrt{(1-cos15)/2}$=$sqrt{(1- sqrt{(1-cos30)/2})/2 } = sqrt{(1- sqrt{(1- sqrt{3 } /2)/2)}$=$sqrt{(1- sqrt{(2- sqrt{3)}/4 })/2 } = sqrt{(1- sqrt{(2- sqrt{3} )} /2)/2} = sqrt{(2- sqrt{2- sqrt{3} }) }$/2=1/2$sqrt{2- sqrt{2- sqrt{3} } }$
sin75=sin(90-15)=cos15=$sqrt{(1+cos30)/2} = sqrt{(1+ sqrt{3} /2)/2} = sqrt{(2+ sqrt{3} )/4} =1/2 sqrt{2+ sqrt{3} }$
2+log(2)sin7гр15мин-log(1/2)cos15гр=2+log(2)sin7гр15мин+log(2)cos15гр=
=
2+log(2)1/2+1/2log(2)(2-$sqrt{2- sqrt{3} } )+log(2)1/2+1/2log(2+ sqrt{3} )=2-1-1+1/2log(2- sqrt{2- sqrt{3} })(2+ sqrt{3})=1/2log(2)( 4-2 sqrt{3} -2 sqrt{2- sqrt{3} } - sqrt{6-3 sqrt{3} } )$