 Hi and welcome to this session. I am Priyanka and let us discuss the following question. Hey, find the general solution for each of the following equation. This is the fifth equation which is given to us cos p8 plus cos x minus cos 2x is equal to 0. First of all we will be applying the formula of cos a plus cos b in order to proceed on to the next step. It is 2 cos a plus p by 2 where a is 3x and b is x. We have 3x plus x by 2 cos 3x minus x by 2 and we have cos 2x above equal to 0. Further let us solve it. We have 2 cos 3x plus x is 4x, 4x divided by 2 by 2, 2x cos x minus cos 2x equal to 0. Now let us take cos 2x common and we are left with 2 cos x minus 1 is equal to 0. So we have further cos 2x divided by equal to 0 or 2 cos x minus 1 is equal to 0. Let us solve it. We have cos 2x is equal to 0 that means 2x is equal to 2n plus 1 multiplied by 5 by 2 which gives us that x is equal to 2n plus 1. Now the 2 will be in the denominator hence pi by 4x. Whereas if 2 cos x minus 1 is equal to 0 that means cos x is equal to 1 by 2 that is equal to cos 6c is equal to cos pi by 3 and hence x is equal to 2n pi plus minus pi by 3. So our answer is the value of x is equal to 2n plus 1 multiplied by pi by 4 or 2n pi plus minus pi by 3 where n belongs to red. Right, so this completes the question that we have given to you. I hope you enjoyed the session today.