Find the value of `x` in the interval `[-pi/2,(3pi)/2\ ]` for which `sqrt(2)sin2x+1lt=2sinx+sqrt(2\ )cosx`

Find the value of x in [-pi,pi] for which f(x)=sqrt(log_(2)(4sin^(2)x-2sqrt(3)sin x-2sin x+sqrt(3)+1)) is defined.

Find the set of all x in (-(pi)/(2),(pi)/(2)) which satisfy | 4 sin x-1| lt sqrt(5)

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

The maximum value of f(x)=(sin2x)/(sinx+cosx) in the interval (0, (pi)/(2)) is

For x in(-pi,pi) find the value of x for which the given equation (sqrt(3)sin x+cos x)^(sqrt(sqrt(3)sin2x-cos2x+2))=4 is satisfied.

Evaluate the value of lim_(n rarr(pi)/(2))tan^(2)x sqrt((2sin^(2)x+3sin x+4)-sqrt(sin^(2)x+sin x+2))

Find the values of A and B if the following function is continuous on [-pi,pi]. f(x) = {((2sinx-sin2x)/x^3,; -pi lt= x lt 0), (Asinx + B cosx,; 0 lt= x lt= pi/2), ((cosecx-1)/(pi//2-x)^2,; pi/2 lt x lt= pi):}