 Hi and welcome to the session. The question says, find a general solution of the following equations. Now the seventh equation given to us is, sin 2x plus cos x is equal to 0. Let us proceed on with our solution. First of all we need to factorize this equation and then find out the general solution of this equation. So now here we can write sin 2x as 2 sin x cos x, right? You remember the identities I hope, plus cos x is equal to 0. Taking cos x common we have in the bracket 2 sin x plus 1 and now we have reached to position to find out the two different values of x where first of all cos x is equal to 0 or 2 sin x plus 1 is equal to 0. On simplifying we have x over here as 2n plus 1 pi by 2 and here on simplifying we have the value of sin x as minus 1 by 2 which says that x is equal to 7 pi by 6. Therefore x is equal to n pi plus minus 1 to the power n 7 pi by... So the general solution of the equation is x is equal to 2n plus 1 multiplied by pi by 2 or n pi plus minus 1 raised to the power n 7 pi by 6. Wait, so this completes the question that was given to us. I hope you enjoyed the session. Bye for now.