 Hello and welcome to the session. I am Arsha and I am going to help you with the following question that says, prove that cos 9x minus cos 5x upon sin 17x minus sin 3x is equal to minus sin 2x upon cos 10x. Let us now begin with the solution and the left hand side is equal to cos 9x minus cos 5x upon sin 17x minus sin 3x. Now simplify it and show that it is equal to the right hand side. Now as we know cos a minus cos p is equal to minus 2 sin a plus b upon 2 into sin a minus b upon 2 and sin a minus sin p is equal to 2 sin a minus b upon 2 into cos a plus b upon 2. So applying these two formulas on the left hand side it can further be written as in the numerator applying the formula cos a minus cos b where a is minus and b is 5x we have in the numerator minus 2 sin a plus b is 9x plus 5x which is equal to 14x upon 2 gives 7x into sin a minus b upon 2. So 9x minus 5x is 4x upon 2 is 2x so we have sin 2x. Now in the denominator applying the formula sin a minus sin b and where a is 17x and b is 3x. So now applying the formula we have 2 sin and we have a minus b. So on subtracting 3x from 17x we get 14x and dividing 14x by 2 gives 7x into cos a plus b is 17 plus 3 into x is equal to 20x upon 2 that will give us 10x. Now on simplifying it further sin 7x cancels out 2 also cancels out and we have minus sin 2x upon cos 10x which is the right hand side of the given problem. Thus we have LHS is equal to the RHS or we can say that cos 9x minus cos 5x upon sin 17x minus sin 3x is equal to minus sin 2x upon cos 10x hence proved. That completes the solution hope you enjoyed it take care and have a good day.