JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Let \(\mathrm{M}\) and \(\mathrm{m}\) respectively be the maximum and minimum values of the function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) in \(\left[0, \frac{\pi}{2}\right]\), Then the value of \(\tan (\mathrm{M}-\mathrm{m})\) is equal to:
- A \(2+\sqrt{3}\)
- B \(2-\sqrt{3}\)
- C \(3+2 \sqrt{2}\)
- D \(3-2 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(3-2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Let \(g(x)=\sin x+\cos x=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)\) \(g(x) \in[1, \sqrt{2}]\) for \(x \in[0, \pi / 2]\) \(f(x)=\tan ^{-1}(\sin x+\cos x) \in\left[\frac{\pi}{4}, \tan ^{-1} \sqrt{2}\right]\)…
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