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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 45 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 45 maths textbook solution

Answers (1)

Answer:

        cos(a-b)log\left | sin(x+b) \right |-xsin(a-b)+C

Hint:

        cos(A+B)=cosAcosB-sinAsinB

Given:

        \int \! \frac{cos(x+a)}{sin(x+b)}dx

Explanation:

        =\int \! \frac{cos(x+a-b+b)}{sin(x+b)}dx        ...adding and subtracting b in numerator

        =\int \! \frac{cos(x+b+a-b)}{sin(x+b)}dx

        =\int \! \frac{cos(x+b)cos(a-b)-sin(x+b)sin(a-b)}{sin(x+b)}dx

        =\int \! cot(x+b)cos(a-b)dx-\int \! sin(a-b)dx

        =cos(a-b)\int \! cot(x+b)dx-sin(a-b)\int \!dx

        =cos(a-b)log\left | sin(x+b) \right |-xsin(a-b)+C

Posted by

Gurleen Kaur

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