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Find the indefinite integration of sin x(x-a)/sin (x+a)

Find the indefinite integration of sin x(x-a)/sin (x+a) 
 

Grade:11

1 Answers

Arun
25757 Points
4 years ago
Please check, it should be sin(x-a) /sin(x+a)
 
sin (x-a) 
= sin (x+a - a -a) 

= sin [(x+a) - 2a] 

= sin (x+a) cos 2a - cos (x+a) sin 2a 

now, question 
= sin (x+a) cos 2a - cos (x+a) sin 2a 
--------------------------------------... 
sin (x+a) 

= cos 2a - sin 2a * cot (x+a) 

integrating abv , we get 

= cos 2a * x - sin 2a log | sin (x+a)| + c

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