 Hello friends. So welcome to another session on trigonometric identity problem solving. So in this problem, it is asked to prove that cosecant theta minus sine theta times secant theta minus cosecant, sorry, cos theta times tan theta plus cot theta is equal to one. The product of these three factors is one. Now, we learned that we have multiple approaches to solve a particular problem. We should keep in mind that either we can reduce it to the most simplest form that is sine and cos and then attempt to the problem or we keep in mind our trigonometric identities, the three basic fundamental relations which we learned. What all did we learn? We learned cos square theta plus sine square theta is equal to one. This is what we learned first. Then we learned cosecant square theta minus cot square theta is equal to one. And then we learned cosecant square theta minus tan square theta is equal to one. These three trigonometric relations we have to keep in mind and a set of trigonometric, sorry, algebraic identities which can be used. Most importantly, things like a square minus b square is equal to a minus b and a plus b. So we have to keep these things in mind before attempting to prove the identity. Now, in this case, in the LHS, if you observe, these two t ratios are reciprocals, isn't it? Secant is the reciprocal of cos and is the reciprocal of cot and cosecant is reciprocal of sine. Can we reduce it to the basic form? Let us try that. So what I'm doing is I'm writing cosecant as, so here is the LHS. So in LHS, I can write cosecant theta as one upon sine theta, one upon sine theta and then sine theta is left as it is. Secondly, this is one upon cos theta and this is cos theta and tan can be written as sine by cos, sine by cos and cot can be written as cos theta upon sine theta. These ratios you must be aware of. Now, taking the LCM, so hence sine theta and here what is the denominator one? Here it is one. So what can I say? This is sine theta is the denominator in the first term, first factor. So hence it is one minus sine square theta. Now the moment you see some kind of form like this one minus sine theta one upon sine theta, it should come automatically in your mind that after reducing it, you will get one minus sine square which is somewhat here, isn't it? If you see one minus sine square is cos square. So that's what is the indication. Now second is similar to the first one. One minus cos square theta by cos theta and then the final one is the LCM is sine theta and cos theta product. And hence the first term is sine square theta and the second term is since sine theta is already here, so hence I have to multiply the top one by cos, so becomes cos square theta. Now it is very, very simple. You could have guessed by now that all the top numerators, the three numerators are related to this particular identity. So hence our life becomes much easier. So one minus sine square can be now written as cos square theta and the denominator is sine theta. Next factor is one minus cos square is sine square theta and the denominator is cos theta. So what is sine square plus cos square? From here it is one, so I will write one upon sine theta times cos theta. So hence this cos square will go because of this cos and this cos and this sine square will go this sine and this sine. So hence eventually it is reduced to one which is equal to RHS. So what did we learn in this question? The learning is if you know it helps to reduce into the basic form but it is not necessary that if you reduce the identity in sine and cos it will become easier. You have to also keep in mind the three identities which I have written on the right hand side and the algebraic identities which will be useful in solving the identities, trigonometric identities. Thank you.