The solution set of `x in (-pi,pi)` for the inequality `sin2x+1lt=cosx+2sinx` is: `x in [0,pi/6]` (b) `x in [pi/6,(5pi)/6]uu{0}` `x in [-pi/6,(6pi)/6]` (d) None of these

The solution set of x in(-pi,pi) for the inequality sin 2x+1 le cosx+2sin x is

sin^-1 (sin ((7pi)/6))= (A) (7pi)/6 (B) pi/6 (C) -pi/6 (D) none of these

The range of f(x)=sin^(-1)((x^(2)+1)/(x^(2)+2)) is [0,(pi)/(2)] (b) (0,(pi)/(6))( c) [(pi)/(6),(pi)/(2)](d) none of these

If 0 <= x <= pi, then the solution of the equation 16^(sin^2) x + 16 ^(cos^2) x = 10 is given by x equal to (i) pi/6,pi/3 (ii) pi/3,pi/2 (iii) pi/6,pi/2 (iv) none of these

Which of the following is not the solution of the equation sin5x=16sin^(5)x(n in Z)?n pi(b)n pi+(pi)/(6)(c)n pi-(pi)/(6) (d) none of these

The value of c in Lagranges theorem for the function f(x)=log sin x in the interval [(pi)/(6),(5 pi)/(6)] is (pi)/(4) (b) (pi)/(2)(2 pi)/(3) (d) none of these

int_(0)^(pi/6) sin2x . cosx dx

The sum of all x in [0,pi] which satisfy the equation sin x+(1)/(2)cos x =sin^(2)(x+(pi)/(4)) is - (A) pi/6 (B) (5pi)/6 (C) pi (D) 2pi

If the angle between the vectors veca=hat i+(cos x)hat j+hat k and vec b=(sin^2 x-sin x)hat i-(cos x)hat j+(3-4sin x)hat k is obtuse and x in (0,pi/2) , then the exhtuse and austive set ofvalues of 'x' is equal to (A) x in (0,pi/6) (B) x in (pi/6,pi/2) (C) x in (pi/6,pi/3) (D) x in (pi/3,pi/2)

If (sin pi)/(6)+(sec pi)/(6)=x, then x is