CBSE Class 12-science Answered
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 | 20 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 | 20 Jun, 2013, 05:35: AM
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