 Hi and welcome to the session. I'm Sian Khan and I will discuss the following question. It says, find the general solution for each of the following phases. And the equation which is given to us is sin x plus sin t x plus sin 5 is to be equal to 0. Before proceeding on with the solution, you should be well aware with the formula that is sin a plus sin b. The formula is 2 sin a plus b by 2 a minus b by 2. The knowledge of this formula is with the idea that we are going to use in order to proceed on with our solution. c x plus sin 5 x to be equal to 0. We will be adding sin x with sin 5 x because on that addition we will get 6 x which on dividing by 2 will result into c x. Right? So we have sin x plus sin 5 x in one bracket plus sin c x to be equal to 0. Further? I'm using the formula that is sin x plus sin b. We have 2 sin a plus b by 2 where a is 5 x and b is 5. a is x and b is 5 x. So we have x plus 5 x divided by 2 plus x minus 5 x divided by 2 and c x is equal to 0. Further? Now we have 2 sin x plus 5 x becomes 6 x. 6 x divided by 2 is p x. cos minus 4 x divided by 2 is minus 2 x plus sin p x equal to 0. or 2 sin p x cos of minus x is cos x only so we have cos 2 x plus sin p x to be equal to 0. Taking sin p x common we are left with 2 cos 2 x plus 1 to be equal to 0. So now we can say that if sin p x is equal to 0 or if 2 cos 2 x is plus 1 is equal to 0. So sin p x is equal to 0 that means p x is equal to n pi that means x is equal to n pi by 3. Whereas cos p x is equal to minus 1 by 2 which means that now cos 2 x can be written as i minus pi by 3 that is the value minus 1 by 2 is cos 2 pi by 3. So 2 x is equal to 2 n pi plus minus 2 pi by 3 and hence the solution is the value of x is equal to pi by 3. The second is also value given to us. Now here 2 x is equal to 2 n pi by 3 so it can be written as x is equal to dividing by each term it is n pi plus minus pi by 3. So it will be plus minus pi by 3 where n belongs to x. So this is our final answer that was the general solution of the equation that was given to us. I hope you enjoyed the session. Take care.