 Hello students let's work out the following problem it says prove that sin theta plus cos theta upon sin theta minus cos theta plus sin theta minus cos theta upon sin theta plus cos theta is equal to 2 secant square theta upon transfer theta minus 1. So let's now move on to the solution and let us proceed on with the solution and let us first simplify the LHS which is sin theta plus cos theta upon sin theta minus cos theta plus sin theta minus cos theta upon sin theta plus cos theta. Now to simplify this we will take the LCM so LCM is sin theta minus cos theta into sin theta plus cos theta. So now in the numerator we have sin theta plus cos theta into sin theta plus cos theta that is we are multiplying sin theta plus cos theta by sin theta plus cos theta similarly sin theta minus cos theta into sin theta minus cos theta. Now again this is equal to sin theta plus cos theta into sin theta plus cos theta is sin theta plus cos theta whole square plus sin theta minus cos theta whole square upon sin theta minus cos theta into sin theta plus cos theta is sin square theta minus cos square theta here we have used the formula a square minus b square is equal to a minus b into a A plus V, whenever you use a formula you must write that. Now in the numerator we will apply the formula of A plus V whole square and A minus V whole square. So this becomes sine square theta plus cos square theta plus 2 sine theta cos theta. A plus V whole square is A square plus B square plus 2 AB. Similarly A minus B whole square is A square plus B square here A is sine theta, B is cos theta minus 2 AB sine square theta minus cos square theta. Now we see that sine square theta plus cos square theta is 1 plus 2 sine theta cos theta plus again sine square theta plus cos square theta is 1 minus 2 sine theta cos theta upon sine square theta minus cos square theta. Now we see that 2 sine theta cos theta gets cancelled with minus 2 sine theta cos theta and in the numerator we have 1 plus 1 that is 2 upon sine square theta minus cos square theta. Now if we see the RHS we need to have tan square theta in the denominator and secant square theta in the numerator. So looking at the RHS we'll divide both numerator and the denominator by cos square theta to get tan square theta here. So we have 2 upon cos square theta upon sine square theta minus cos square theta upon cos square theta right. Now this becomes 2 secant square theta because 1 upon cos square theta is secant square theta and here we have sine square theta upon cos square theta minus cos square theta upon cos square theta. So this is equal to 2 secant square theta upon sine square theta upon cos square theta is tan square theta minus cos square theta upon cos square theta is 1 and here you have to write that 1 upon cos theta is secant theta and here also you need to write the identity which you are using that the sine square theta plus cos square theta is 1 and this is what we had to prove and this is the RHS hence proved. That's the question and the session. Why fun or take care. Have a good day.