 Hi and welcome to the session. I am Deepika here. Let's discuss a question using the fact that sign of a plus b is equal to sine a cos b plus cos is sine b and the differentiation Open the sum formula for cosines. So let's start the solution We are given the fact sine a plus b is equal to sine a cos b plus cos a sine b Now on differentiating both sides with respect to x with respect to x we have cos a plus b into d by dx of a plus b is equal to Now again for this term, we will apply the project rule. So this is sine a into d by dx of cos b plus cos b into d by dx of sine a Plus Again here apply the product rule cos a into d by dx of sine b plus sine b into d by dx of cos a Now on the left hand side we have cos a plus b into d a by dx plus d b by dx This is equal to Now sine a into derivative of cos b that is minus sine b into d b by dx minus sine a sine b into d b by dx plus cos b into cos a into d a by dx plus cos a into cos b into d b by dx sine b into minus of sine a into d a by dx This is minus sine b sine a into d a by dx This is equal to Now d b by dx into cos a cos b minus sine a sine b plus d a by dx into Now d a by dx into cos b cos a cos a minus sine b sine a therefore cos a plus b into d a by dx plus d b by dx is equal to again d b by dx plus d a by dx into cos a cos b minus sine a sine b We have cos of a plus b cos a cos b minus sine a sine b Hence by using the sine formula that is sine of a plus b is equal to sine a cos b plus cos a sine b and the differentiation We open the some formula for cosine, which is cos of a plus b is equal to cos a cos b minus sine a sine b I hope the question is clear to you. Bye and have a nice day