if integration of sin x/sin (x-a) dx=Ax+B log(sin(x-a))+c then the value of (A,B) is????

Asked by shashank tripathi | 20th Jun, 2013, 04:09: AM

Expert Answer:

Since, integration of sin x/sin (x-a) dx=Ax+B log(sin(x-a))+c
 
Hence,  sin x/sin (x-a)  = d(Ax+B log(sin(x-a))+c)/dx 
sin x/sin (x-a)  = A+Bcos(x-a)/sin(x-a) 
sin x/sin (x-a)  = [Asin(x-a)+Bcos(x-a)]/sin(x-a) 
So, sinx = Asin(x-a)+Bcos(x-a)
Now, if A = cosa and B = sina
RHS=  cos(a)sin(x-a)+sin(a)cos(x-a)
= sin(x-a+a)
= sinx  = LHS
 
hence, A = cosa and B = sina

Answered by  | 20th Jun, 2013, 05:35: AM

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