Question

已知(a^2)/9+(b^2)/4=1,(c^2)/9+(d^2)/4=1,且ac+bd=0,求证(a^2+b^2)(c

Answer 1

a=3cosA,b=2sinA,c=3cosB,d=2sinB 9cosAcosB+4sinAsinB=0 tanAtanB=-9/4

(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2=(ac+bd)^2-2acbd+a^2d^2+b^2c^2

=(ad-bc)^2=【6sin(B-A)]^2