Solve the following questions
Ex.1 . Solve the following into partial fractions Ex.2 Find the equation of the circumcircle of the triangle formed by 2x+y=4, x+2y=5 and x+y=6 Ex.3 Solve the following inequality log(x -2)+log(9 -x)<1 Ex.4 If and are two vectors such that then find the angle between and . Ex.5. Solve the following trigonometric equation, Ex. 6 Find the equation of the tangent to the circle at (1, - 2) .Verify that this line also touches the circle . Find also the point of contact. Ex. 7Find, f(A), if A= and f(x) = EX.8 32 22 4 20 7 ( 1) ( 8) x x x xx a b a b a b a b 2 tan cot 1, 0 2 22 5 xy 22 8 6 20 0 x y x y 1 2 2 ( 4 3 4 ) 4 4 5 2 1 x x 5 7 5 ( 0 4 1 ) 2 8 3 B (I) Find the determinant of the matrix B. (II) Given that f( ) (the determinant of B) satisfies the equation f(A)=0, find the inverse of A.