Question

$\mathrm{If}x=a\sin \theta \mathrm{and}y=b\cos \theta ,\mathrm{then}\mathrm{write}\mathrm{the}\mathrm{value}\mathrm{of}\left(b^2{x}^2+a^2{y}^2\right).$

Answer 1

$$\begin{gathered} \left(b^2{x}^2+a^2{y}^2\right) \\ =b^2{\left(a\sin \theta \right)}^2+a^2{\left(b\cos \theta \right)}^2 \\ =b^2{a}^2{\sin }^2\theta +a^2{b}^2{\cos }^2\theta \\ =a^2{b}^2\left({\sin }^2\theta +{\cos }^2\theta \right) \\ =a^2{b}^2\left(1\right) \\ =a^2{b}^2 \end{gathered}$$