Solve `|[y,sinx,cosx] , [cosx,1,y] , [-sinx,-y,1]|`

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

Solve sinx+cosx=1+sinx.cosx

If |[cosx, sinx, cosx], [-sinx, cosx, sinx], [-cosx, -sinx, cosx]|=0 , then x=

Solve : 4sinx cosx +2sinx+2cosx+1=0

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

Solve: sinx+cosx=(sqrt3+1)/4

If y=|[sinx, cosx, sinx],[cosx,-sinx,cosx],[x,1,1]| then find (dy)/(dx)

The area under the curve y=sinx , y=cosx , y-axis is A_1 , y=sinx , y=cosx , x-axis is A_2 then A_1:A_2 is

F(x)=[[cosx,-sinx,0],[sinx,cosx,0],[0,0,1]] and G(x)=[[cosx,0,sinx],[0,1,0],[-sinx,0,cosx]], then [F(x)G(y)]^(-1) is equal to (A) F(-x)G(-y) (B) F(x-1)G(y-1) (C) G(-y)F(-x) (D) G(y^(-1))F(x^(-1))