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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 5 maths textbook solution

Answers (1)

Answer:

            2sin\: x-log\left | sec\: x+tan\; x \right |+C

Hint:

            sec\: x=\frac{1}{cos\: x}

Given:

        \int \frac{sec\: x}{sec\: 2x }dx

Explanation:

        \int\left(\frac{1}{\cos x}\right)\left(\frac{1}{\frac{1}{\cos 2 x}}\right) d x

       =\int\! \frac{cos\: 2x}{cos\: x}dx

       =\int\! \frac{2cos^{2}\: x-1}{cos\: x}dx

       =\int\!2\frac{cos^{2}x}{cos\: x}dx-\frac{1}{cos\: x}dx

       =2\! \int\!cos\: xdx-\int\! sec\: xdx

       =2 sin\; x-log\left | sec\: x +tan\: x\right |+C

Posted by

Gurleen Kaur

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