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प्रश्न
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
उत्तर
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,
\[b^2 x^2 + a^2 y^2 = a^2 b^2\]
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