If x = a sin θ and y = b cos θ, write the value of (b 2 x 2 + a 2 y 2 ).

Question

Philoid · Accepted Answer

Given: x = a sin θ

y = b cos θ

Then b²x² + a²y² = b²(a sin θ)² + a²(b cos θ)²

= a²b² sin² θ + a² b² cos² θ

= a²b² (sin² θ + cos² θ)

= (a²b²) × 1

= a²b²