AP EAMCET · Maths · Differentiation
If \(y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right)\), then \(\frac{d y}{d x}\) is
equal to
- A 0
- B \(\frac{a}{b}\)
- C -1
- D 2
Answer & Solution
Correct Answer
(C) -1
Step-by-step Solution
Detailed explanation
\(y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right)\) \[ =\tan ^{-1}\left(\frac{\frac{a}{b-\tan x}}{1+\frac{a}{b} \tan x}\right) \] [Take \(b \cos x \operatorname{common}\) from numerator and denominator]…
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