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Solution for If − π 2 < X < 0 and Y = Tan − 1 √ 1 − Cos 2 X 1 + Cos 2 X , Find D Y D X ? - CBSE (Science) Class 12 - Mathematics

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Question

If \[- \frac{\pi}{2} < x < 0 \text{ and y } = \tan^{- 1} \sqrt{\frac{1 - \cos 2x}{1 + \cos 2x}}, \text{ find } \frac{dy}{dx}\] ?

Solution

\[\text{ We have, y } = \tan^{- 1} \sqrt{\frac{1 - \cos2x}{1 + \cos2x}}\]

\[ \Rightarrow y = \tan^{- 1} \sqrt{\frac{2 \sin^2 x}{2 \cos^2 x}}\]

\[ \Rightarrow y = \tan^{- 1} \sqrt{\tan^2 x}\]

\[ \Rightarrow y = \tan^{- 1} \left( \tan x \right) \left[ \because \tan^{- 1} \left( \tan x \right) = - x , if x \in \left( - \frac{\pi}{2}, 0 \right) \right]\]

\[ \Rightarrow y = - x\]

\[\Rightarrow \frac{dy}{dx} = - 1\]

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Solution If − π 2 < X < 0 and Y = Tan − 1 √ 1 − Cos 2 X 1 + Cos 2 X , Find D Y D X ? Concept: Simple Problems on Applications of Derivatives.
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