Let \[ I = \int {\frac{{\cos x - \cos 2x}}{{1 - \cos x}}} dx = \int {\frac{{2\sin \frac{{3x}}{2} \cdot \sin \frac{x}{2}}}{{1 - 1 + 2{{\sin }^2}\frac{x}{2}}}} dx\]


\[ = 2\int {\frac{{\sin \frac{{3x}}{2} \cdot \sin \frac{x}{2}}}{{2{{\sin }^2}\frac{x}{2}}}} dx = \int {\frac{{\sin \frac{{3x}}{2}}}{{\sin \frac{x}{2}}}} dx\]

\[ = \int {\frac{{3\sin \frac{x}{2} - 4{{\sin }^3}\frac{x}{2}}}{{\sin \frac{x}{2}}}} dx\]

\[ = 3\int d x - 4\int {{{\sin }^2}} \frac{x}{2}dx = 3\int d x - 4\int {\frac{{1 - \cos x}}{2}} dx\]

\[ = 3\int d x - 2\int d x + 2\int {\cos } xdx\]

\[ = \int d x + 2\int {\cos } xdx = x + 2\sin x + C = 2\sin x + x + C\]

Buy Best Mathematics E-Books Visit : https://mathstudy.in/

Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/

Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/

Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/

Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/