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  • Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 6

Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 6

Answers (1)

Answer:

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

Hint:

            cos^{2}\: x-sin^{2}\: x=cos2x

Given:

            \int\! \frac{cos2x}{(cos\: x+sin\: x)^{2}}dx

Explanation:

\int\! \frac{cos^{2}-sin^{2}x}{(cos\: x+sin\: x)^{2}}dx

=\int\! \frac{(cos\: x+sin\: x)(cos\: x-sin\: x)}{(cos\: x+sin\: x)^{2}}dx

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

Let \; \; cos\: x+sin\: x=t

(-sin\: x+cos\: x)dx=dt

=\int \! \frac{1}{t}dt

=log\left | t \right |+C

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

Posted by

Gurleen Kaur

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