Question

If x = m sin theta and y = n cos theta, then find the value of n²x²
+ m²y²​

Answer 1

Answer:

(mn)²

Step-by-step explanation:

Given, x = m sinθ

y = n cosθ

sinθ = x/m

cosθ = y/n

∵ cos²θ + sin²θ = 1

=> y²/n² + x²/m² = 1

=> x²n² + y²m²/m²n² = 1

=> x²n² + y²m² = m²n²

=> n²x² + m²y² = (mn)²

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Answer 2

Answer:

(mn)²

Step-by-step explanation:

Given, x = m sinθ

y = n cosθ

sinθ = x/m

cosθ = y/n

∵ cos²θ + sin²θ = 1

=> y²/n² + x²/m² = 1

=> x²n² + y²m²/m²n² = 1

=> x²n² + y²m² = m²n²

=> n²x² + m²y² = (mn)²