Question

if x cos theta minus y sin theta is equal to a, x sin theta + y cos theta is equal to b prove that x square plus y square is equal to a square + b square

Answer 1

Given (2 cosθ - sinθ) = x and (cosθ - 3 sinθ) = y. Put the values of x and y in 2x2 + y2 − 2xy (LHS) = 2(2 cosθ − sinθ)2 + (cosθ − 3 sinθ)2 − 2(2 cosθ − sinθ)(cosθ − 3 sinθ) = 2(4cos2θ − 4cosθ sinθ + sin2θ) + (cos2θ − 6cosθ sinθ + 9sin2θ) ...