`2{(sqrt(3)+2)sinx+2cosx}` lies in the interval

sqrt(3) sinx + cosx = sqrt(2)

Find the solutions of the equation , log_(sqrt2sinx)(1+cosx)=2 in the interval x in[0,2pi].

One root of the equation cosx-x+1/2=0 lies in the interval

The number of distinct real roots of the equation |{:(cosx, sinx, sinx), (sinx, cosx, sinx), (sinx, sinx, cosx):}|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

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 .

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 =|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 log_(cosx) sinx>=2 and x in [0,3pi] then sinx lies in the interval

The number of distinct roots of |(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx,cosx,sinx)|=0 in the interval -pi/4 le x le pi/4 is (A) 0 (B) 2 (C) 1 (4) 2