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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]]

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)

If F (x) = [[cos x,-sin x,0],[sin x, cos x, 0],[0,0,1], then show that F(x) F(y)= F (x+y).

F(x) =[[cos x, -sin x, 0],[ sin x, cos x, 0],[ 0, 0, 1]] Show that F(x) F(y)=F(x+y)

Let f(x)= [[cos x, -sin x, 0],[sin x, cos x, 0],[0,0,1]] ,Show that f (x) f(y)= f(x+y) .

If f(x)=[[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]] , show that f(x).f(y)=f(x+y)

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to