Question

If x = a cos ø + b sin ø and y = a sin ø-b cos ø,prove that x^2+y^2 = a^2 +b^2.​

Answer 1

Explanation:

x = a cos∅ + b sin∅

y = a sin∅ - b cos∅

$x^2 = a^2 cos^2$∅ + $b^2sin^2$∅ + $2ab sin$∅$cos$∅

$y^2 = a^2 sin^2$∅ $+b^2cos^2$∅ - $2absin$∅$cos$∅

Therefore,

$x^2+y^2 = a^2 (sin$∅$+cos^2$∅) + $b^2(sin^2$∅$+cos^2$∅)

$x^2+y^2=a^2+b^2$