Question

已知xcosγ=a,ycotγ=b（a不等于0,b不等于0）,求证x^2/(a^2)-y^2/(b^2)=1

Answer 1

xcosγ=a,ycotγ=b

x/a=1/cosγ,(x/a)^2=(1/cosγ)^2

y/b=1/cotγ=tanγ=sinγ/cosγ,(y/b)^2=(sinγ/cosγ)^2

x^2/(a^2)-y^2/(b^2)

=(1/cosγ)^2-(sinγ/cosγ)^2

=[1-(sinγ)^2]/(cosγ)^2

=(cosγ)^2/(cosγ)^2

=1