If `0ltalphaltbetaltpi/2` then

If 0ltalphaltbetaltpi/2, show that (sinalpha)/alphagt(sinbeta)/beta

If 0ltalphaltbetaltpi/2 show that alpha-sin alpha lt beta-sinbeta

The vertices of a cube are (0,0,0),(2,0,0),(0,0,2),(0,2,0),(2,0,2),(0,2,2),(2,2,0),(2,2,2) respectively What is the angle between any two diagonals of the cube?

If the matrix A=[[2,0,2] , [0,2,0] , [2,0,02]] then A^n=[[a,0,0] , [0,a,0] , [b,0,a]], n in N where

What is the value of the determinant |[0, 0, 2],[0, 2, 0],[2, 0 ,0]|

The point equidistant from the point (0,0,0),(1,0,0,),(0,2,0) and (0,0,3) is (A) (1/3, 2/3, 2) (B) (1,0,2) e (C) (1/2, 1, 3/20 (D) (-1, 2, 1/2)

[" 2.Let matrix "A=[[1,y,4],[2,2,z]]" ; if "xyz=2 lambda" and "8x+4y+3z=lambda+28," then "(adj A)" A equals: "],[[" (A) "[[lambda+1,0,0],[0,lambda+1,0],[0,0,lambda+1]]," (B) "[[lambda,0,0],[0,lambda,0],[0,0,lambda]]],[" (C) "[[lambda^(2),0,0],[0,lambda^(2),0],[0,0,lambda^(2)]]," (D) "[[lambda+2,0,0],[0,lambda+2,0],[0,0,lambda+2]]]]

The incentre of triangle whose vertices are P(0, 2, 1), Q(-2, 0, 0), R(-2, 0, 2)

If A=[[0,0] , [2,0]] then show that A^2=0