 Hello and welcome to the session. I am Ashima and I am there to help you with the following problem. Prove that the determinant with elements x sin theta cos theta minus sin theta minus x1 cos theta 1 and x is independent of theta. Now let us write the solution. Let us first find the value of determinant. So we have delta is equal to the determinant with elements x sin theta cos theta minus sin theta minus x1 cos theta 1 and x. Now let us solve this determinant which is equal to now x multiplied by determinant minus x1 1 x minus sin theta multiplied by determinant minus sin theta 1 cos theta and x plus cos theta multiplied by determinant minus sin theta minus x cos theta and 1. Now solving it further is equal to x multiplied by minus x square minus 1 minus sin theta multiplied by minus x sin theta minus cos theta plus cos theta multiplied by minus sin sin theta plus x cos theta. Now solving it further we get now opening the bracket so we get minus x cube minus x plus x sin square theta plus sin theta cos theta plus x cos square theta minus sin theta cos theta. Now we will see that this gets cantals with this so we get now minus x cube minus x. Now from these two terms taking x common so we get plus x multiplied by sin square theta plus cos square theta which is equal to minus x cube minus x plus x we know sin square theta plus cos square theta is equal to 1 so multiplied by 1 which is equal to minus x cube minus x plus x. Now we see that this and this gets cancels so we are left with minus x cube. Here we can see that this term is independent of theta hence proved. I hope you understood the problem. Bye and have a nice day.