For `0ltxltpi/ 2,` prove that `cos(sinx)gtsin(cosx)`

For 0ltxlt(pi)/(2) ,prove that x gt sin x and hence cos (sin x) gt sin (cosx)

Integrate (sinx)/((sinx-cosx))dx=?

If x+y+z=pi/2, then prove that |[sinx,siny,sinz],[cosx,cosy,cosz],[cos^3x,cos^3 y,cos^3z]|=0

For each natural number nlt=2, prove that sinx_1cosx_2+sinx_2c0sx+3++sinx_ncosx_1lt=n/2 (where x_1, x_2, ,x_n are arbitrary real numbers).

Prove that sin1>cos(sin1)dot Also, show that the equation sin("cos"(sinx))=cos("sin"(cosx)) has only one solution in [0,pi/2]dot

If x in (0,pi//2)a n dcosx=1//3 , then prove that sum_(n=0)^oo(cosn x)/(3^n)=(3(3-cosx))/(10-6cosx+cos^2x)

Evaluate int(dx)/(2+sinx+cosx).

If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)

Prove that sinx +sin2x +sin3x =sin2x (1+2cosx) .

Integrate the functions (sinx)/((1+cosx)^(2))