If x = √(a^(sin⁻¹ t)), y = √(a^(cos⁻¹ t)), then dy/dx is:
If x = √(a^(sin⁻¹ t)), y = √(a^(cos⁻¹ t)), then dy/dx is:
- A. −y/x
- B. y/x
- C. x/y
- D. −x/y
Answer: A) −y/x
Explanation: x = a^((1/2) sin⁻¹ t), y = a^((1/2) cos⁻¹ t). Multiply: xy = a^((1/2)(sin⁻¹ t+cos⁻¹ t)) = a^(π/4) constant. So xy = c. Differentiating: x y′ + y = 0 → y′ = −y/x.
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