 Hello and welcome to the session. Let's work out the following question. It says prove the following identity where the angles involved are acute angles for which the expression is defined. So let's now move on to the solution and let's start with LHS which is tan theta upon 1 minus cot theta plus cot theta upon 1 minus tan theta. Now we'll simplify LHS this is equal to tan theta can be written as sin theta upon cos theta upon 1 minus cot theta which can be written as cos theta upon sin theta plus cot theta is cos theta upon sin theta upon 1 minus tan theta and tan theta is sin theta upon cos theta. Now we have sin theta upon cos theta into taking LCM and then simplifying we have sin theta upon sin theta minus cos theta plus here also we'll take LCM here and we'll multiply this with the reciprocal of this. So we have cos theta upon sin theta into cos theta upon cos theta minus sin theta. So this is equal to sin square theta upon cos theta into sin theta minus cos theta plus cos square theta upon sin theta into cos theta minus sin theta is again equal to sin square theta upon cos theta into sin theta minus cos theta minus here we take minus common so we have cos square theta upon sin theta into sin theta minus cos theta now taking LCM so LCM would be sin theta cos theta into sin theta minus cos theta and in the numerator we have sin cube theta minus cos cube theta now again this is equal to here we'll apply the formula of a cube minus b cube which is a minus b into a square plus a b plus b square so the numerator will become sin theta minus cos theta into a square here a is sin theta and b is cos theta plus sin square theta plus a b b is cos theta so it is sin theta into cos theta plus cos square theta upon sin theta into cos theta into sin theta minus cos theta sin theta minus cos theta gets cancelled with sin theta minus cos theta and let's write the formula we have used now this is equal to sin square theta plus cos square theta plus sin theta cos theta upon sin theta cos theta now we know that sin square theta plus cos square theta is equal to 1 so this is 1 plus sin theta cos theta upon sin theta into cos theta is again equal to 1 upon sin theta into 1 upon cos theta plus sin theta cos theta upon sin theta cos theta sin theta gets cancelled with sin theta cos theta gets cancelled with cos theta and we have left with 1 upon sin theta is cos square theta 1 upon cos theta is sin theta plus 1 so this is equal to 1 plus sin theta into cos theta and which is the RHS hence proved so this completes the question on the session bye for now take care have a good day