Question Number 61147 by malwaan last updated on 29/May/19
$$\boldsymbol{{prove}} \\ $$$$\int\frac{\mathrm{1}+{cos}\:{x}}{\mathrm{1}−{cos}\:{x}}{dx}=−\mathrm{2}{cot}\:\frac{{x}}{\mathrm{2}}−{x}+{c} \\ $$$$ \\ $$
Answered by tanmay last updated on 29/May/19
$$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$$$\int\left({cosec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}−\mathrm{1}\right){dx} \\ $$$$=\frac{−{cot}\left(\frac{{x}}{\mathrm{2}}\right)}{\frac{\mathrm{1}}{\mathrm{2}}}−{x}+{c} \\ $$$$=−\mathrm{2}{cot}\left(\frac{{x}}{\mathrm{2}}\right)−{x}+{c} \\ $$
Commented by malwaan last updated on 29/May/19
$${thank}\:{you}\:{sir} \\ $$$${can}\:{you}\:{solve}\:{it}\:{by}\:{trig}.\:{sub}.\:? \\ $$