Show that `5xlt=8sinx-sin2xlt=6xfor0lt=xlt=pi/3dot`

Show that 2sinx+tanxgeq3x ,w h e r e0lt=x

Discuss the extremum of f(x)=sinx+1/2sin2x+1/3sin3x ,0lt=xlt=pidot

Find the value of "cos"(2cos^(-1)x+sin^(-1)x) at x=1/5, where 0lt=pi and -pi/2lt=sin^(-1)xlt=pi/2dot

Find the coordinates of the points of intersection of the curves y=cosx , y=sin3x if-pi/2lt=xlt=pi/2

Discuss the extremum of f(x)=1+2sinx+3 cos^2x ,xlt=xlt=(2pi)/3

Let S be the area bounded by the curve y=sinx(0lt=xlt=pi) and the x-axis and T be the area bounded by the curves y=sinx(0lt=xlt=pi/2),y=acosx(0lt=xlt=pi/2), and the x-axis (w h e r ea in R^+) The value of (3a) such that S : T=1:1/3 is______

Solve the equation 2(cos x+cos2x)+sin2x(1+2cos x)=2sinx for (-pilt=xlt=pi)

Number of solutions of the equation sin^4x-cos^2xsinx+2sin^2x+sinx=0in0lt=xlt=3pi is_____

If f(x)=int_(0)^(pi)(t sin t dt)/(sqrt(1+tan^(2)xsin^(2)t)) for 0lt xlt (pi)/2 then