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).

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)

Inverse of f(x) = [(cos x , sin x, 0),(-sin x, cos x, 0),(0,0,1)] is

if f(x) = (x-1)/(x+1), x ne -1 , then show that : f(f(x)) = -1/x, x ne 0 .

If f(x) = |(sin x, cos x , tan x),(x^3, x^2 ,x),(2x, 1,x)| then Lim_(x to 0) (f(x))/(x^2) equals

Let f(x) = |{:(2cos ^(2) x,,sin 2x,,-sin x),(sin 2x,,2 sin^(2)x,,cos x),(sin x,,-cos x,,0):}| .then the value of int_(0)^(pi//2) [ f(x) +f'(x) ] dx " is "

If f (x) = (sin [x])/([x]) for [x] ne 0. Then lim _(x to 0_(-)) f (x) equals :

If f(x) = (sin 2x + A sin x + B cos x)/(x^(3)) is continuous at x = 0. Find the values of A and B. Also, find f(0)

If f and g are continuous functions on [0,a] satisfying f(x)=(a-x) and g(x)+g(a-x)=2 , then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx .