Grade 11Integral Calculus
Find the indefinite integration of sin x(x-a)/sin (x+a)
Find the indefinite integration of sin x(x-a)/sin (x+a)
1 Answer
Arun
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
= 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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