Solve the following determinant : `|(1,x,y),(0,cos x,sin y),(0,sin x,cos x)|`

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

Prove that |(1,x,1),(0,cos x, sin y),(0 , sin x, cos y )|=cos (x+y)

Prove that |(1,x,y),(0, sin x, sin y),(0, cos x,cos y)|= sin (x-y)

Solve the following differential equation: (dy)/(dx)+(cos x sin y)/(cos y)=0

Solve the following differential equations x cos x (dy)/(dx)+y(x sin x+ cos x)=1 .

If x , y in R , then the determinant = |(cos x , -sin x,1),(sin x, cos x,1),(cos(x+y), -sin(x+y), 0)| lies in the interval (a) [-sqrt(2),sqrt(2)] (b) [-1,1] (c) [-sqrt(2),1] (d) [-1,-sqrt(2)]

Solve the following differential equation (6)cos x cos y dy-sin x sin y dx=0

Solve the following differential equation: cos x cos y(dy)/(dx)=-sin x sin y

Solve the following differential equations. (e^y+1)cos x dx+e^y sin x dy=0