Mathematics

Solve:$$\int \dfrac{\cos x}{1+\cos x}.dx$$


SOLUTION
$$\int { \dfrac { \cos x }{ 1+\cos x } dx } \\ =\int { \dfrac { 2{ \cos }^{ 2 }\dfrac { x }{ 2 } -1 }{ 2{ \cos }^{ 2 }\dfrac { x }{ 2 }  } dx } \quad (\because \cos2x=2{ \cos }^{ 2 }x-1)\\ =\int { \left[ 1-\dfrac { 1 }{ 2{ \cos }^{ 2 }\dfrac { x }{ 2 }  }  \right] dx } \\ =\int { \left[ 1-\dfrac { 1 }{ 2 } { \sec }^{ 2 }\dfrac { x }{ 2 }  \right] dx } \\ =x-\dfrac { 1 }{ 2 } .2\tan\dfrac { x }{ 2 } +C\\ =x-\tan\dfrac { x }{ 2 } +C$$
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Subjective Medium Published on 17th 09, 2020
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