Question

X=a sinA, y=b tanA.prove that a square/x square - b square/y square=1

Answer 1

x=asinA, y=btanA
∴, a²/x²-b²/y²
=a²/a²sin²A-b²/b²tan²A
=1/sin²A-1/tan²A
=1/sin²A-1/(sin²A/cos²A)
=1/sin²A-cos²A/sin²A
=(1-cos²A)/sin²A
=sin²A/sin²A [∵, sin²A+cos²A=1]
=1 (Proved)