If `P(x) = [(cosx, sinx), (-sinx, cosx)]` then show that `P(x)P(y)=P(x+y)=P(y)P(x)`

If P(x)=[[cos x,sin x-sin x,cos x]] then show that P(x)P(y)=P(x+y)=P(y)P(x)

If P(x)=[cos x sin x-sin x cos x], then show that P(x)P(y)=P(x+y)=P(y)P(x)

If f(x) = [(cos x , - sinx,0),(sinx,cosx,0),(0,0,1)] then show f(x) . f(y) = f(x+y)

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

If y=|[sinx, cosx, sinx],[cosx,-sinx,cosx],[x,1,1]| then find (dy)/(dx)

if y=(sinx+cosx)/(sinx-cosx) , then (dy)/(dx) at x=0 is equal to

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

If y=(sinx)/(1+(cosx)/(1+(sinx)/(1+(cosx)/(1+ tooo)))),p rov et h a t(dy)/(dx)=((1+y)cosx+ysinx)/(1+2y+cosx-sinx)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)