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

Evaluate the following determinants. [[1,x,y],[0,sinx,siny],[0,cosx,cosy]]

Evaluate the following determinants: |(sinx,cosx,sinx+cosx),(siny, cosx, sin y + cosx),(sinz,cosx, sinz+cosx)|

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

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

If, x,y inR , then the determinant: Delta=|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)| lies in the interval .