The value of $\int \mathrm{e}^x\left(\frac{1-\sin x}{1-\cos x}\right) \mathrm{dx}$ is equal to
- A$-\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)
- B$\mathrm{e}^x \cot \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)
- C$\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$,(where c is a constant of integration)
- D$-\mathrm{e}^x \operatorname{cosec} \frac{x}{2}+\mathrm{c}$, (where c is a constant of integration)
✓ Correct answer: A
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