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17/01/2022 3:14 pm
Topic starter
If y(x) = cot-1 \(\Big(\frac{\sqrt{1+sinx}+\sqrt{1-sinx}}{\sqrt{1+sinx} - \sqrt{1-sinx}}\Big)\), x ∈ \(\Big(\frac{\pi}{2}, \pi\Big)\), then \(\frac{dy}{dx}\) at x = \(\frac{5 \pi}{6}\) is
(1) \(-\frac{1}{2}\)
(2) -1
(3) \(\frac{1}{2}\)
(4) 0
1 Answer
1
17/01/2022 3:18 pm
Correct answer: (1) \(-\frac{1}{2}\)
Explanation:
y(x) = cot-1\(\Big[\frac{cos \frac{x}{2} + sin \frac{x}{2}+sin \frac{x}{2} - cos \frac{x}{2}}{cos \frac{x}{2} + sin \frac{x}{2} - sin \frac{x}{2} + cos \frac{x}{2}}\Big]\)
y(x) = cot-1\(\Big(tan \frac{x}{2}\Big)\) = \(\frac{\pi}{2}\) - \(\frac{x}{2}\)
y'(x) = \(-\frac{1}{2}\)