The equation `4sin^2x-2\ (sqrt(3)+1)sinx+sqrt(3)=0`
(a) 2 solution in `(0,\ pi)`
(b) 4 solution in `(0,\ 2pi)`
(c) 2 solution in `(-pi\ pi)`
(d) 4 solution in `(-pi\ pi)`

Solutions of sin^(-1) (sinx) = sinx are if x in (0, 2pi)

Statement-1: The number of |cosx | = sinx in [0,4pi] is 4 Statement-2: The equation sin^(2)x -1/sqrt(2) (sqrt(3)+1) sinx + sqrt(3)/4=0 has two roots in [0,pi/2] . Statement-3:The number of solutions of sin theta + sin 5theta= sin 3theta, theta in [0,pi] is 5.

The solution of the equation sin^-1((tan)pi/4)-sin^-1(sqrt(3/x))-pi/6=0 is

find the number of solution of sin^(2) x-sin x-1=0 in [-2pi, 2pi] .

The least positive solution of cot(pi/(3sqrt3) sin2x)=sqrt3 lie (a) (0,pi/6) (b) (pi/9,pi/6) (c) (pi/12,pi/9) (d) (pi/3,pi/2)

For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4 (c) (3pi)/4 (d) (4pi)/3

Number of roots of cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0 which lie in the interval [-pi,pi] is 2 (b) 4 (c) 6 (d) 8

Number of roots of cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0 which lie in the interval [-pi,pi] is 2 (b) 4 (c) 6 (d) 8

The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx) ,for x in (pi/4,pi/2) (b) cosx+sinx ,for x in (0,pi/4) (c) -(cosx+sinx) ,for x in (0,pi/4) (d) cosx-sinx ,for x in (pi/4,pi/2)