 Hello and welcome to the session. Let us understand the following problem today. Evaluate determinant with elements cos alpha cos beta cos alpha sin beta minus sin alpha minus sin beta cos beta 0 sin alpha cos beta sin alpha sin beta and cos alpha. Now let us write the solution. We have determinant which is equal to cos alpha cos beta cos alpha sin beta minus sin alpha minus sin beta cos beta 0 sin alpha cos beta sin alpha sin beta cos alpha. Now expanding it along row R1 let us expand it along this row. So we get it is equal to cos alpha cos beta now eliminating this row and eliminating this column and now solving the determinant we get cos beta cos alpha minus 0 Now minus cos alpha sin beta for this eliminating this column and this row we get multiplied by sin beta cos alpha that is minus sin beta cos alpha minus 0 Now minus sin alpha for this eliminating this row and this column so we get minus sin alpha sin square beta minus sin alpha cos square beta. Now solving it further which is equal to cos alpha cos beta into cos alpha cos beta is equal to cos square alpha cos square beta. Now cos alpha cos beta multiplied by 0 is equal to 0 so minus 0 then minus cos alpha sin beta multiplied by minus sin beta cos alpha we get plus cos square alpha sin square beta minus cos alpha sin beta multiplied by 0 is equal to plus 0 then minus sin alpha multiplied by sin alpha sin square beta is equal to plus sin square alpha sin square beta Similarly here we get plus sin square alpha cos square beta. Now now taking cos square alpha from these two terms common we get cos square alpha multiplied by sin square beta plus cos square beta plus now taking sin square alpha common from these two so we get sin square alpha multiplied by sin square beta plus cos square beta. Now using the identity sin square theta plus cos square theta is equal to 1 we get it is equal to cos square alpha multiplied by 1 plus sin square alpha multiplied by 1 which is equal to cos square alpha plus sin square alpha which is equal to 1 therefore 1 is our required answer. I hope you understood this problem bye and have a nice day.