Mathematics

# If $\int \frac { 1 } { 5 + 4 \cos 2 \theta } d \theta = A \tan ^ { - 1 } ( B \tan \theta ) + c$ then $( A , B ) =$

##### SOLUTION
$\begin{array}{l} \int { \frac { { d\theta } }{ { 5+4\cos 2\theta } } =\int { \frac { { d\theta } }{ { 5+\frac { { 4\left( { 1-\tan \theta } \right) } }{ { 1+{ { \tan }^{ 2 } }\theta } } } } } } \\ =\int { \frac { { { { \sec }^{ 2 } }\theta d\theta } }{ { 9+{ { \tan }^{ 2 } }\theta } } } \\ Let\, \tan \theta =u \\ \frac { { du } }{ { d\theta } } ={ \sec ^{ 2 } }\theta \\ Now, \\ =\int { \frac { { du } }{ { 9+{ u^{ 2 } } } } =\frac { 1 }{ 3 } { { \tan }^{ -1 } }\left( { \frac { { \tan \theta } }{ 3 } } \right) +C } \\ \left( { A\, ,B } \right) =\left( { \frac { 1 }{ 3 } ,\, \frac { 1 }{ 3 } } \right) \end{array}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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