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

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)

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

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) is continuous at x = 0 , find a, where f(x) = {{:((1 - cos ax)/(x sin x)"," , x != 0),(1/2",", x = 0 ):}

Solve the equation sin x + cos x -2sqrt2 sin x cos x =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

Find k in R if f(x) = {:{((cos^2 x - sin^2 x -1)/(sqrt(x^2+1) - 1), x ne 0), (k, x = 0):} is continuous at 0.

Solve the equation ( cos x - sin x )(2 tan x +(1)/( cos x ))+2 =0