来自唐广波的问题
【证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4】
证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4
1回答
2020-03-08 10:04
【证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4】
证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4
sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)
=sin^2(x)+cos(x+30)[cos(x+30)+sinx]
=sin^2(x)+cos(x+30)(cosxcos30-sinxsin30+sinx)
=sin^2(x)+cos(x+30)(cosxcos30+1/2*sinx)
=sin^2(x)+cos(x+30)(cosxcos30+sinxsin30)
=sin^2(x)+(cosxcos30-sinxsin30)(cosxcos30+sinxsin30)
=sin^2(x)+cos^2(x)*(cos30)^2-(sin30)^2*sin^2(x)
=3/4*cos^2(x)+sin^2(x)-1/4*sin^2(x)
=3/4*cos^2(x)+3/4*sin^2(x)=3/4