If y = tan⁻¹((a cos x − b sin x)/(b cos x + a sin x)), then dy/dx is: A. −1 B. 1 C. 0 D. −2 Answer: A) −1 Explanation: Put a = r cos α, b = r sin α. Then expression = tan⁻¹((r cos(α+x))/(r sin(α+x))) = tan⁻¹(cot(α+x)) = π/2 − (α+x). So y′ = −1.

imo class 12 continuity and differentiability

If y = tan⁻¹((a cos x − b sin x)/(b cos x + a sin x)), then dy/dx is:

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If y = tan⁻¹((a cos x − b sin x)/(b cos x + a sin x)), then dy/dx is:

Answer: A) −1

Explanation: Put a = r cos α, b = r sin α. Then expression = tan⁻¹((r cos(α+x))/(r sin(α+x))) = tan⁻¹(cot(α+x)) = π/2 − (α+x). So y′ = −1.