Question

докажите тождество
1+2cos2x=4cos(30+x)cos(30-x)

Answer 1

2cos(30+x)cos(30-x)=4*1/2*[cos(30+x-30+x)+cos(30+x+30-x)]=
=2(cos2x+cos60)=2cos2x+2*1/2=2cos2x+1