 I am welcome to the session, I am Aushu and I am going to help you with the following problem that says proof that sin square pi upon 6 plus cos square pi upon 3 minus tan square pi upon 4 is equal to minus half. Let us begin with the solution and we will find the value of left hand side and show that its value is equal to minus half. Left hand side is sin square pi upon 6 plus cos square pi upon 3 minus tan square pi upon 4 which can further be written as sin pi upon 6 whole square plus cos pi upon 3 whole square minus tan pi upon 4 whole square. Sin pi upon 6 is sin 30 degree plus cos pi by 3 is cos 60 degree whole square minus tan pi by 4 is tan 45 degree whole square. Now sin 30 degree is half with half whole square plus cos 60 degree is again half minus tan 45 degree is 1. So it can further be written as 1 upon 4 plus 1 upon 4 minus 1. Now in adding these two we get 1 upon 2 minus 1 which is further equal to minus half which is equal to the right hand side of the given equation and thus we have LHS is equal to RHS and hence we have proved that sin square pi upon 6 plus cos square pi upon 3 minus tan square pi upon 4 is equal to minus half. This completes the solution. Hope you enjoyed it. Take care and have a good day.