Question

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

Answer 1

Answer:

The value of b²x² + a²y²  is a²b².

Step-by-step explanation:

Given : x = a sin θ and y = b cos θ

On Substituting the values of x and y in the given expression b²x² + a²y²,  

b²x² + a²y² = b²(a sin θ)² + a²(b cos θ)²

= b²a²sin²θ + a²b²cos²θ

= a²b²(sin²θ + cos²θ)

= a²b² × 1

[By using the identity , sin² θ + cos² θ = 1]

b²x² + a²y² = a²b²

Hence, the value of b²x² + a²y²  is a²b².

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Answer 2

Answer:

a²b²

Step-by-step explanation:

Given: x = a sinθ

y = b cosθ

Now,

b²x² + a²y² (given)

Putting given values in it, we get

→ b²(a sinθ)² + a²(b cosθ)²

→ b²(a²sin²θ) + a²(b²cos²θ)

→ a²b²sin²θ + a²b²cos²θ

→ a²b²(sin²θ + cos²θ)

→ a²b²(1)

{ Identity : sin²θ + cos²θ = 1 }

→ a²b²