 Hello and welcome to the session. The given question says, evaluate integral sin x-alpha divided by sin x-alpha into dx. Let's start with the solution and here we are given integral sin x-alpha divided by sin x-alpha into dx. So let us denote it by i. So this is equal to i. Now next we shall substitute x-alpha is equal to t. So on differentiating both sides we have dx divided by dt is equal to 1 on differentiating both sides with respect to t and on cross multiplying this further implies that dx is equal to dt. So x-alpha can be written as x plus alpha minus alpha minus alpha and here x plus alpha is equal to t minus 2 alpha. Therefore sin x-alpha is equal to sin t minus 2 alpha. Therefore integral i can further be written as sin t minus 2 alpha divided by sin t into dt. Since dx is equal to dt now as we know sin a minus b is equal to sin a into cos b minus cos a into sin p. Therefore this can further be written as integral sin t into cos 2 alpha minus cos t into sin 2 alpha whole divided by sin t into dt. This is further equal to integral sin t into cos 2 alpha divided by sin t into dt minus integral cos t into sin 2 alpha divided by sin t into dt. This is further equal to sin t cancels out with sin t taking cos 2 alpha outside the integral sin we have integral 1 into dt minus taking sin 2 alpha outside the integral sin we have cos t divided by sin t into dt. Now let us take x is equal to sin t so this implies dx is equal to cos t into dt. So this can further be written as cos 2 alpha integral 1 dot dt is t minus sin 2 alpha integral dx divided by x which further implies cos 2 alpha into t minus sin 2 alpha and integral dx divided by x is log mod x plus a constant c. This is further equal to cos 2 alpha into t minus sin 2 alpha into log x is sin t so we have log mod sin t plus a constant c. Now let us substitute the value of t which has x plus alpha. So here we have x plus alpha into cos 2 alpha minus sin 2 alpha into log mod sin x plus alpha plus a constant c. Thus on evaluating the given integral we get x plus alpha into cos 2 alpha minus sin 2 alpha into log mod sin x plus alpha plus a constant c. So this completes the session. Bye and take care.