 Hi and welcome to the session. Let us discuss the following question which says prove that cot a minus cos a upon cot a plus cos a is equal to cosecant a minus 1 upon cosecant a plus 1. Before moving on to the solution let's see the key idea that we will be using for this question. For some angle theta first of all we have cot theta is equal to cos theta upon sine theta and cosecant theta is equal to 1 upon sine theta. Let's move on to the solution. We need to prove cot a minus cos a upon cot a plus cos a is equal to cosecant a minus 1 upon cosecant a plus 1. So let us start with LHS which is equal to cot a minus cos a upon cot a plus cos a. In the key idea we have already learnt that cot theta is equal to cos theta upon sine theta. So here let us change cot a to cos a upon sine a so this will be equal to cos a upon sine a minus cos a upon cos a upon sine a plus cos a. Now in numerator and denominator both let us take cos a common so this will be equal to cos a into 1 upon sine a minus 1 upon cos a into 1 upon sine a plus 1. Now here cos a will get cancelled in the numerator and denominator and thus we are left with 1 upon sine a minus 1 upon 1 upon sine a plus 1. Now from the key idea we know that cosecant theta is equal to 1 upon sine theta so here 1 upon sine a will be equal to cosecant a and thus this will be equal to cosecant a minus 1 upon cosecant a plus 1 which is equal to RHS. So here we started from LHS and we got RHS that means LHS is equal to RHS that is cot a minus cos a upon cot a plus cos a is equal to cosecant a minus 1 upon cosecant a plus 1 hence proved. With this we finish this session hope you must have understood the question goodbye take care and have a nice day.