If `A=[(2,0,0),(0,cos,sinx),(0,-sinx,cosx)]` then `(AdjA)^-1=` (A) `1/2A` (B) A (C) 2A (D) 4A

If A=[(cosx,sinx),(-sinx,cosx)] and A.(adjA)=k[(1,0),(0,1)] then the value of k is

If A=[(cosx,sinx),(-sinx,cosx)] and A.(adjA)=k[(1,0),(0,1)] then the value of k is

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

If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to (a) 1/2 (b) 0 (c) 1 (d) none of these

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

If 16cotx=12 , then (sinx-cosx)/(sinx+cosx) equals (a) 1/7 (b) 3/7 (c) 2/7 (d) 0

The value of |(cos(x-a), cos(x+a), cosx),(sin(x+a), sin(x-a), sinx),(cosatanx, cosacotx, cosec2x)|= (A) 1 (B) sina cosa (C) 0 (D) sinx cosx

If cosx+cosy+cosz=sinx+siny+sinz=0" then "cos(x-y)= (a) 0 (b) -1/2 (c) 2 (d) 1

If sinx, cosx, tanx are in G.P., then cot^6x-cot^2x= (A) 0 (B) -1 (C) 1 (D) depends on x

The number of solutions of the equation |cosx-sinx|=2cosx in [0,2pi] is (A) 1 (B) 2 (C) 3 (D) 4