Question

Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?

Options

• \[\sin a\int dt-\cos a\int\cot t\,dt\]

• \[\cos a\int\tan t\,dt-\sin a\int dt\]

• \[\cos a\int\cot t\,dt-\sin a\int dt\]

• \[\cos a\int dt-\sin a\int\cot t\,dt\]

Answer 1

Divide \[\sin t\cos a-\cos t\sin a\] by \[\sin t\]. This gives \[\cos a-\sin a\cot t\], which is then integrated term by term.