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

find the value for x F(x)=|[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]|

Let F(x)= [cosx -sinx 0 sinx cosx 0 0 0 1] . Show that F(x)\ F(y)=F(x+y)

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)=[("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

Given that F(x)=[{:(,cos x,-sin x,0),(,sin x,cos x,0),(,0,0,1):}]."If"in R Then for what values of y, F(x+y)=F(x)F(y)

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), sin(x-x^2)],[sin2x,0,sin(2x^2)]| . Find the value of f^(prime)(0) .

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).