 Hello and welcome to the session. Let's work out the following question. It says evaluate the following expression. So let's move on to the solution and let us first discuss the first part. The given expression is sin square 63 degrees plus sin square 27 degrees upon cos square 17 degrees plus cos square 73 degrees. Now we know that cos square theta plus sin square theta is equal to 1 and we also know that cos 90 minus theta is equal to sin theta and sin 90 minus theta is cos theta. Now here we see that the sum of the angles in the numerator and also in denominator is 90 degrees. So we convert one of the sin theta's in the numerator to cos theta and in the denominator we'll convert one of the cos theta's into sin theta using these two rules. So we have sin square 63 degrees plus sin square 27 degrees can be written as 90 degrees minus 63 degrees upon cos square 17 degrees plus cos square 73 degrees can be written as cos square 90 minus 17 degrees. This is further equal to sin square 63 degrees plus cos square 63 degrees as we know that sin 90 minus theta is cos theta upon cos square 17 degrees plus sin square 17 degrees. Using this rule cos 90 minus theta is sin theta. Now cos square theta plus sin square theta is 1. So we have one in the numerator and one in the denominator. So the answer is 1. Let's now discuss the second part. The given expression is sin 25 degrees into sin 65 degrees plus cos 25 degrees into sin 65 degrees. Now here again we see that some of the angles here and here also is 90 degrees. So we'll convert one of the sin theta here into cos theta but here we have cos 65 degrees not sin 65 degrees. Let us cos 65 degrees. So we'll convert cos 65 degrees into sin 25 degrees and here we'll convert sin 65 degrees into cos 25 degrees using these two rules again. So we have sin 25 degrees into cos 65 degrees which can be written as cos 90 degrees minus 25 degrees plus cos 25 degrees and sin 65 degrees can be written as sin 90 minus 25 degrees. So again this is equal to sin 25 degrees into sin 25 degrees since cos 90 minus theta is sin theta and here we have cos 25 degrees into cos 25 degrees since sin 90 minus theta is cos theta. This is equal to sin square 25 degrees plus cos square 25 degrees and again using the formula sin square theta plus cos square theta is 1 so this is equal to 1. So answer to the first part of the question is 1 and to the second part also answer is 1. So this completes the question on the session. Bye for now. Take care. Have a good day.