已知(x/a)cosθ+(y/b)sinθ=1,(x/a)sinθ-(y/b)cosθ=1,求证(x^2/a^2)+(y^2/b^2)=2如题示.

问题描述:

已知(x/a)cosθ+(y/b)sinθ=1,(x/a)sinθ-(y/b)cosθ=1,求证(x^2/a^2)+(y^2/b^2)=2
如题示.

(x/a)cosθ+(y/b)sinθ=1
[(x/a)cosθ+(y/b)sinθ]^2=1
(x/a)sinθ-(y/b)cosθ=1
[(x/a)sinθ-(y/b)cosθ]^2=1
[(x/a)cosθ+(y/b)sinθ]^2+[(x/a)sinθ-(y/b)cosθ]^2=(x^2/a^2)+(y^2/b^2)=2