Solve the following determinant : `|(1,x,y),(0,cosx,siny),(0,sinx,cosy)|`

Solve the following determinant : det[[1,x,y0,cos x,sin y0,sin x,cos y]]

Solve the following determinant : det[[1,x,y0,cos x,sin y0,sin x,cos x]]

Solve the following differential equation: cosx(1+cosy)dx-siny(1+sinx)dy=0

If x epsilon R the determinant Delta=|(1,cosx,0),(-1,1-cosx,sinx+cosx),(0,-1,1-sqrt(2)sin(x+pi//4))| equals

Solve the following inequations (i) (sinx-2)(2sinx-1) lt 0 (ii) (2cosx-1)(cosx) le 0 (iii) sinx+sqrt(3)cosx ge 1 (iv) cos^(2)x+sinx le 2 (v) tan^(2)x gt 3

Find the general solution of each of the following differential equations: cosx(1+cosy)dx -siny (1+sinx)dy =0

(cosx)^(y)=(siny)^(x)

The number of distinct roots of |(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx,cosx,sinx)|=0 in the interval -pi/4 le x le pi/4 is (A) 0 (B) 2 (C) 1 (4) 2

Find the inverse matrix of the matrix A=|{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}|