AP EAMCET · Maths · Differentiation
If \(y=\cos ^{-1}\left\{\frac{a \cos x-b \sin x}{\sqrt{a^2+b^2}}\right\}\), then \(\frac{d^2 y}{d x^2}\) is equal to
- A \(a-b\)
- B \(a+b\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
We have, \(y=\cos ^{-1}\left(\frac{a \cos x-b \sin x}{\sqrt{a^2+b^2}}\right)\) \(y=\cos ^{-1}(\cos (x-\theta))\left[\because\right.\) where, \(\left.\theta=\tan ^{-1} b / a\right]\) \(\begin{aligned} & y=x-\theta \\ & y=x-\tan ^{-1} b / a \Rightarrow d y / d x=1\end{aligned}\)…
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