If `f(x) =|{:(sinx,cosx,sinx),(cosx,-sinx,cosx),(x,1,1):}|` find the value of `2[f'(0)]+[f'(1)]^(2)`

If A=[{:(cosx,sinx),(-sinx,cosx)] then find |A|

int (2cosxdx)/(sinx+cosx)

Expand | (cosx, -sinx),(sinx , cosx)|

int (2sinx-cosx)/(2cosx+sinx)dx =

int (sinx-cosx)/(cosx+sinx)dx =

The number of distinct real roots of |(sinx,cosx,cosx),(cosx, sinx,cosx),(cosx,cosx,sinx)|=0 in the interval (-pi)/4lexlepi/4 is :

int dx/(1-cosx -sinx) =

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

If sin2x=1 , then |(0,cosx,-sinx),(sinx,0,cosx),(cosx,sinx,0)| equals :

If y=(sinx+cosx)/(sinx-cosx) find (dy/dx) ?