Prove that the equation `2 sin x=|x|+a` has no solution for `a in ((3sqrt(3)-pi)/3, oo)`.

Prot that the equation k cos x-3sin x=k+1 possess a solution if k in (-oo,4] .

The equation |"sin" x| = "sin" x + 3"has in" [0, 2pi]

Solve the equation sqrt3cos x + sin x = sqrt2 .

Solve the equation sqrt3cos x + sin x = sqrt2 .

Solve the equation sqrt3 cos x + sin x =1 for - 2pi lt x le 2pi.

Find number of solution of the equation 2 sin x+5 sin^(2) x+8sin^(3)x+... oo=1 for x in [0, 2pi] .

Find the solution of the equation ( sin x + cos x ) sin 2 x =a(sin^(3) x + cos^(3) x) located between (pi)/(2) and pi and for which values of 'a' does this equation have at most one solution satisfying the condition (pi)/(2) le x le pi .

Number of solutions of the equation 2 sin^3x + 6 sin^2x -sin x-3=0 in (0, 2pi), are

The solutions of the system of equations sin x sin y=sqrt(3)/4, cos x cos y= sqrt(3)/4 are

For x in (0,pi) the equation sinx+2sin2x-sin3x=3 has