If `F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)]`, show that `F(x) F(y)=F(x+y)`.

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

If A=[(cosx,sinx),(-sinx,cosx)] , show that A^(2)=[(cos2x,sin2x),(-sin2x,cos2x)] and A^(1)A=1 .

int_0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =

If sin2x=1 , then |(0,cosx,-sinx),(sinx,0,cosx),(cosx,sinx,0)| equals :

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 .

If Delta(x)=|(1,cosx,1-cosx),(1+sinx,cosx,1+sinx-cosx),(sinx, sinx ,1)| then int_0^(pi//2)Delta(x) dx is equal to :

If f(x) = [((sin [x])/([x]), [x] ne 0),(0, [x] = 0)] , then lim_(x rarr 0) f(x) is :

If f(x)={((1-cosx)/(x),xne0),(k, x=0):} is continuous at x=0 then k=

If y=(sinx)^(cosx)+x^(sinx) find dy/dx.