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Evaluate :
           \int \frac{\cos 2x+2\sin ^{2}x}{\cos ^{2}x}dx

 

 

 

 
 
 
 
 

Answers (1)

\int \frac{\cos 2x+2\sin ^{2}x}{\cos ^{2}x}dx= \int \frac{\cos ^{2}x-\sin ^{2}x+2\sin ^{2}x}{\cos ^{2}x}dx
                                                                    \left [ \because \cos 2x= \cos ^{2}x-\sin ^{2}x \right ]
                                         = \int \frac{\cos ^{2}x+\sin ^{2}x}{\cos ^{2}x}dx
                                         = \int \frac{1}{\cos ^{2}x}dx= \int \sec ^{2}x\, dx
                                         =\tan x+c

Posted by

Ravindra Pindel

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