Question

if x=a cos theta - b sin theta and y=a sin theta b cos theta,then prove that a^2 b^2=x^2 y^2

Answer 1

acosα -bsinα = x
asinα - bcosα = y

squaring both the equations and adding

a²cos²α + b²sing²α -2absinαcosα = x²
a²sin²α + b²cos²α + 2absinαcosα = y²

a² + b² = x² + y²
thus proved.