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Evaluate \[\int \text{cosec} x\cot x\,dx\]

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Question

Evaluate \[\int \text{cosec} x\cot x\,dx\]

Options

  • \[-\text{cosec} x+\mathrm{C}\]

  • \[\text{cosec} x+\mathrm{C}\]

  • \[-\cot x+\mathrm{C}\]

  • \[\sec x+\mathrm{C}\]

MCQ
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Solution

The derivative of \(-\text{cosec} x\) is \(\text{cosec} x\cot x\). Thus, \(\int \text{cosec} x\cot x\,dx=-\text{cosec} x+\mathrm{C}\).

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