作业帮证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/02 17:13:15
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
=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
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