Question

Compute
\[\int\frac{\sin(x+a)}{\sin(x+b)}\]

Answer 1

watchmath can you take a look at the following while I attempt this?:

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4dee61954c0e8b0b8965cdd8

Answer 2

take sin(x+a)=sin((x+b)+(b-a))=sin(x+b)cos(b-a)+cos(x+b)sin(b-a)\[\int\limits_{}^{}\frac{\sin(x+a)}{\sin(x+b)}=\int\limits (\cos(b-a)+\sin(b-a)\cot(x+b))dx\]

Answer 3

\[=\cos(b-a)x+\sin(b-a)\ln (\sin(x+b))+c\]

Answer 4

hmm algebraic typo there \(x+a\neq x+b+b-a\)

Answer 5

sorry b-a will be a-b