 Hi and welcome to the session. I am Deepika here. Let's discuss the question if cos y is equal to x cos a plus y With cos a is not equal to plus minus 1 prove that dy by dx is equal to cos scale a plus y upon sine x So let's sign a So let's start the solution given cos y is equal to x cos a plus y This implies x is equal to cos y upon cos a plus y on differentiating with respect to y and Using quotient rule we have dx by dy is Equal to here. We will apply the quotient rule that is cos a plus y Into derivative of cos y that is minus sine y minus Cos y into derivative of cos a plus y that is minus of sine a plus y upon cos square a plus y so dx by dy is equal to minus sine y cos a plus y plus cos y Into sine a plus y upon cos square a plus y so This is again equal to dx by dy is equal to cos sine a plus y into cos y minus cos a plus y into sine y upon cos square a plus y So here use a formula sign a minus b is sine a Into cos b minus cos a into sine b. So this is equal to sine of a plus y minus y upon cos square a plus y so this is equal to sine a upon cos square a plus y therefore dy by dx is equal to cos square a plus y Upon sine a Hence we have proved that if cos y is equal to x cos a plus y with cos a is not equal to plus minus 1 Then dy by dx is equal to cos square a plus y upon sine a I Hope the question is clear to you. Bye and have a nice day