If `x in [0, 2pi]` for which `2cosx<=|sqrt(1+sin2x)-sqrt(1-sin2x)|<=sqrt(2)` has solution set `x in [(lambdapi)/4,(mupi)/4]` then value of `lambda+mu` is

Let f(x) = ((cosx+|cosx|)(sinx - 3/2)^3 (tanx-1)^5)/((cosx-2)^2(tanx-sqrt(3))^3) Find the interval of x in (-pi/2, pi/2) for which (i) f(x) > 0(ii) f(x) < 0

Number of solution of x; where x in [-2pi,2pi] ; which satisfy equation sinx.cosx=1 is

Number of solution of x; where x in [-2pi,2pi] ; which satisfy equation sinx.cosx=1 is

Statement-I: x inQ_(1) and cosx+cos3x=cos2x then x=30^(@)or45^(@) Statement-II: x in(0,2pi) and Cosecx+2=0 then x=(7pi)/(6),(11pi)/(6) Statement-III: x in[0,2pi] and (2cosx-1)(3+2cosx)=0 then x=(pi)/(3),(5pi)/(3) wich of the above statements is correct?

If s={x in [0,2pi]:|[0,cosx,-sinx],[sinx,0,cosx],[cosx,sinx,0]|=0} then sum_(x in s) tan(pi/3+x) is equal to:

If S={x epsilon [0,2pi]:|(0,cosx,-sinx),(sinx,0,cosx),(cosx,sinx,0)|=0} then sum_(xepsilonS)tan((pi)/3+x) is equal to

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)

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)