If `x , y in R ,` then the determinant `=|cosx-sinx1sinxcosx1cos(x+y)-sin(x+y)0|` lies in the interval `[-sqrt(2),sqrt(2)]` (b) `[-1,1]` `[-sqrt(2),1]` (d) `[-1,-sqrt(2)]`

If x , y in R , then the determinant =|[cosx,-sinx,1],[sinx,cosx,1],[cos(x+y),-sin(x+y),0]| lies in the interval (a) [-sqrt(2),sqrt(2)] (b) [-1,1] (c) [-sqrt(2),1] (d) [-1,-sqrt(2)]

If x , y in R , then the determinant = |(cos x , -sin x,1),(sin x, cos x,1),(cos(x+y), -sin(x+y), 0)| lies in the interval (a) [-sqrt(2),sqrt(2)] (b) [-1,1] (c) [-sqrt(2),1] (d) [-1,-sqrt(2)]

If, x,y inR , then the determinant: Delta=|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)| lies in the interval .

The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the interval [0,pi/2] is (a)4(sqrt(2)-2) (b) 2sqrt(2) ( sqrt(2) -1) (c)2(sqrt(2) +1) (d) 2sqrt(2)(sqrt(2)+1)

The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the interval [0,pi/2] is (a)4(sqrt(2)-2) (b) 2sqrt(2) ( sqrt(2) -1) (c)2(sqrt(2) +1) (d) 2sqrt(2)(sqrt(2)+1)

The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the interval [0,pi/2] is (a)4(sqrt(2)-2) (b) 2sqrt(2) ( sqrt(2) -1) (c)2(sqrt(2) +1) (d) 2sqrt(2)(sqrt(2)+1)

The area enclosed by the curves y=sinx+cosx and y=|cosx−sinx| over the interval [0,pi/2] is (a) 4(sqrt2-1) (b) 2sqrt2(sqrt2-1) (c) 2(sqrt2+1) (d) 2sqrt2(sqrt2+1)

The area enclosed by the curve y=sin x+cos x and y=|cos x-sin x| over the interval [0,(pi)/(2)] is 4(sqrt(2)-2) (b) 2sqrt(2)(sqrt(2)-1)2(sqrt(2)+1)(d)2sqrt(2)(sqrt(2)+1)

y=sin^(-1)((sinx+cosx)/sqrt2)=?