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Log { Cot ( π 4 + X 2 ) } ? - Mathematics

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प्रश्न

\[\log\left\{ \cot\left( \frac{\pi}{4} + \frac{x}{2} \right) \right\}\] ?

बेरीज
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उत्तर

\[\log\left\{ \cot\left( \frac{\pi}{4} + \frac{x}{2} \right) \right\} = \frac{- {cosec}^2 \left( \frac{\pi}{4} + \frac{x}{2} \right)}{2\cot\left( \frac{\pi}{4} + \frac{x}{2} \right)}\]

\[ = \frac{- 1}{2\cos\left( \frac{\pi}{4} + \frac{x}{2} \right)\sin\left( \frac{\pi}{4} + \frac{x}{2} \right)}\]

\[ = \frac{- 1}{\sin\left( \frac{\pi}{2} + x \right)}\]

\[ = \frac{- 1}{\cos x}\]

\[ = - \sec x\]

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Notes

The answer given at the back of the exercise in RD Sharma is incorrect.

  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Differentiation - Exercise 11.02 [पृष्ठ ३८]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 11 Differentiation
Exercise 11.02 | Q 53 | पृष्ठ ३८

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