যদি, \(3x=5sin\theta\) এবং \(4y=5cos\theta\) হয়, তবে নীচের কোন সম্পর্কটি সঠিক ? (a) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=1\) (b) \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=0\) (c) \(\cfrac{9x^2}{25}-\cfrac{16y^2}{25}=1\) (d) \(\cfrac{16x^2}{25}+\cfrac{9y^2}{25}=1\)
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Answer: A
\(3x=5sin\theta\)
বা, \(sin\theta=\cfrac{3x}{5}\)
\(4y=5cos\theta\)
বা, \(cos\theta=\cfrac{4y}{5}\)
আমরা জানি, \(sin^2\theta+cos^2\theta=1\)
বা, \((\cfrac{3x}{5})^2+(\cfrac{4y}{5})^2=1\)
বা, \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=1\)
\(3x=5sin\theta\)
বা, \(sin\theta=\cfrac{3x}{5}\)
\(4y=5cos\theta\)
বা, \(cos\theta=\cfrac{4y}{5}\)
আমরা জানি, \(sin^2\theta+cos^2\theta=1\)
বা, \((\cfrac{3x}{5})^2+(\cfrac{4y}{5})^2=1\)
বা, \(\cfrac{9x^2}{25}+\cfrac{16y^2}{25}=1\)