Solve: `|-2x^2+1+e^x+sinx|=|2x^2-1|+e^x+|sinx|,x in [0,2pi]`.

Solve |sinx+cosx|=|sinx|+|cosx|,x in [0,2pi] .

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

If f(x)=2sinx-x^(2) , then in x in [0, pi]

Solve cos2x >|sinx|,x in (pi/2,pi)

Differentiate the following function with respect to x : sin^(-1)(sinx),x in [0,2pi] cos^(-1)(cosx),x in [0,2pi] tan^(-1)(tanx),x in [0,pi]-{pi/2}

Find the number of solution(s) of following equations: (i) x^(2)-sinx-cosx+2=0 (ii) sin^(2)x - 2sinx - x^(2)-3=0, x in [0,2pi]

Solve 2sinx+cos2x+2sin^(2)x-1 for 0 le x le 2pi .

Solve cos2xgt|sinx|,x in(-(pi)/(2),pi)

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

Separate the intervals of monotonocity for the following function: (a) f(x) =-2x^(3)-9x^(2)-12x+1 (b) f(x)=x^(2)e^(-x) (c ) f(x) =sinx+cosx,x in (0,2pi) (d) f(x) =3cos^(4)x+cosx,x in (0,2 pi) (e ) f(x)=(log_(e)x)^(2)+(log_(e)x)