`(2sinx-cosx)(1+cosx)=sin^2x`

Let alpha be a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 gamma be a root of the equation 1-sin2x=cosx-sinx 0<=alpha,beta,gamma<=pi/2 sin alpha+sin beta+sin gamma can be equal to (A) (14+3sqrt(2))/6 (B) 43226 (C) (3+4sqrt(2))/6 (D) (1+sqrt(2))/2

Let alpha be a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a root of the equation 3cos^2x-10cosx+3=0 gamma be a root of the equation 1-sin2x=cosx-sinx 0<=alpha,beta,gamma<=pi/2 The value of sin (alpha-beta) is equal to (A) 1 (B) 0 (C) (1-2sqrt(6))/6 (D) (sqrt(3)-2sqrt(2))/6

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

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

If int (3sin x+2 cosx)/(3cosx+2sinx)dx=ax+blog_(e)|2 sinx+3 cosx|+c then

If int (3sin x+2 cosx)/(3cosx+2sinx)dx=ax+blog_(e)|2 sinx+3 cosx|+c then

3(sinx-cosx)^4+6(sinx+cosx)^2+4(sin^6x+cos^6x)=

3(sinx-cosx)^4+6(sinx+cosx)^2+4(sin^6x+cos^6x) is equal to