要詳細(xì)過程謝謝

熱心網(wǎng)友

證明：因?yàn)閤+y=3-cos4θ,(1)x-y=4sin2θ (2)所以，(1)+(2)，得2x=3-cos4θ+4sin2θ=2+2(sin2θ)^2+4sin2θ=2(sin2θ+1)^2,所以，x=(sin2θ+1)^2.(1)-(2)，得2y=3-cos4θ-4sin2θ =2+2(sin2θ)^2-4sin2θ=2(sin2θ-1)^2,所以y=(sin2θ-1)^2.所以，x^(1/2)+y^(1/2)=|sin2θ+1|+|sin2θ-1|=1+sin2θ+1-sin2θ,(因?yàn)閟in2θ≥-1,sin2θ≤1)=2.

熱心網(wǎng)友

證明：x+y=3-cos4a,x-y=4sin2a兩式相加、減，分別得2x=3-cos4a+4sin2a2y=3-cos4a-4sin2a而2x=3-cos4a+4sin2a=3-[1-2(sin2a)^2]+4sin2a=2(sin2a)^2+4sin2a+2=(2sin2a+2)(sin2a+1)x=(sin2a+1)^2√x=(sin2a+1)2y=3-cos4a-4sin2a=(2sin2a-2)(sin2a-1)y=(sin2a-1)^2√y=1-sin2a所以√x+√y=sin2a+1+1-sin2a=2