Question

If x = a sin θ and y = b cos θ, what is the value of b²x² + a²y²?

Answer 1

Given:

x = a sinθ and y = b cosθ

So, \[b^2 x^2 + a^2 y^2 = b^2 \left( asin\theta \right)^2 + a^2 \left( bcos\theta \right)^2 \]
\[ = a^2 b^2 \sin^2 \theta + a^2 b^2 \cos^2 \theta\]
\[ = a^2 b^2 \left( \sin^2 \theta + \cos^2 \theta \right)\] 

We know that, `sin^2 θ+cos^2θ=1`

Therefore,

\[b^2 x^2 + a^2 y^2 = a^2 b^2\]