If `f(x)={:[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)]` show that `f(alpha)f(beta)=f(alpha+beta)`.

if f(x) = |{:(sinx,cosx,tanx),(x^3,x^2,x),(2x,1,1):}| then show that lim_(xto0)(f(x))/x^2=1

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

if f(alpha,beta) = |[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[cos(alpha+beta),-sin(alpha+beta),1]| then (a) f(300 , 200)=f(400 , 200) (b) f(200 , 400)=f(200 , 600) (c) f(100 , 200)=f(200 , 200) (d)none of these

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

The function f(x)=(sinx)/(sinx-cosx) is discontinuous at -

If f(x)=|(sinx, cosx, tanx),(x^(3),x^(2),x),(2x,1,1)| then the value of lim_(x to 0) (f(x))/(x^(2)) is -

If f(x)=(x-1)(x-2)(x-3)(x-4) , show that the equation f'(x)=0 has three roots alpha, beta and gamma where 1 lt alpha lt 2, 2 lt beta lt 3 and 3 lt gamma lt 4 .

If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}| , then lim_(xto0)(f(x))/(x^(2))=

Let f(x)= |{:(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0):}| ,"then find " 1/piint_0^(pi/2)[f(x)+f'(x)]dx.