Question

integration 1-cosx/cosx(1+cosx)dx​

Answer 1

Answer:

ANSWER

Given,  ∫  

cosx(1+cosx)

(1−cosx)dx

​  

 

⇒  ∫  

cosx(1+cosx)

(1+cosx)

​  

−  

cosx(1+cosx)

2cosx

​  

dx

⇒  ∫secx−  

1+cosx

2

​  

dx

⇒  ∫secx−  

2cos  

2

 

2

x

​  

 

2

​  

dx       since [cosx=2cos  

2

 

2

x

​  

−1]

⇒  ∫secx−sec  

2

 

2

x

​  

dx

⇒   log(secx+tanx)−2tan  

2

x

​  

+c     is our answer.

Step-by-step explanation:

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