`|[cosx,-sinx],[sinx,cosx]|`

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

If A=[(cosx,-sinx),(sinx,cosx)] , then A A^(T) is

If A=[(cosx,sinx),(sinx,-cosx)] and A("adj "A)=lamda[(1,0),(0,1)] , then lamda is equal to

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

If delta(x)=|[1,cosx,1-cosx],[1+sinx,cosx,1+sinx-cosx],[sinx,sinx,1]|, then int_0^(pi/2)delta(x)dx is equal to

If P(x)=[(cosx, sinx),(-sinx, cosx)] , then show that P(x).P(y)=P(x+y)=P(y).P(x) .

If A=[{:(cosx,sinx,0),(-sinx,cosx,0),(0,0,1):}] =f(x), then A^(-1) is equal to

Find the inverse matrix of the matrix A=|{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}|

If S={x epsilon [0,2pi]:|(0,cosx,-sinx),(sinx,0,cosx),(cosx,sinx,0)|=0} then sum_(xepsilonS)tan((pi)/3+x) is equal to