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  • Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 14

Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 14

Answers (1)

Answer:

        -log\left | sin\; x+cos\: x \right |+C

Hint:

        Cot\: x=\frac{cos\: x}{sin\: x}

Given:

        \int \! \frac{1-cot\: x}{1+cot\: x}dx

Explanation:

        \int \! \frac{1-\frac{cos\: x}{sin\: x}}{1+\frac{cos\: x}{sin\: x}}dx   =\int \! \frac{sin\: x-cos\: x}{sin\: x+cos\: x}dx

 Let

        sin\: x+cos\: x=t

        (cos\: x-sin\: x)dx=dt

        =-\int \! \frac{dt}{t}\; \; \; \; =-log\: t+C

        =-log\left | sin\: x+cos\: x \right |+C

Posted by

Gurleen Kaur

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