Find the values of `a` if equation `1-cosx=(sqrt(3))/2|x|+ a ,x in (0,pi),` has exactly one solution.

Find the value of l'al'so that the equation f(x)=x^(2)+(a-3)x+a=0 has exactly one alpha between the interval (1,2) and f(x+alpha)=0 has exactly one root between the interval (0,1)

Find the value of l'al'so that the equation f(x)=x^(2)+(a-3)x+a=0 has exactly one alpha between the interval (1,2) and f(x+alpha)=0 has exactly one root between the interval (0,1)

The number of solution of sqrt3Cos^2x=(sqrt3-1)Cosx+1 , x in [0,pi/2]

Find the possible values of p such that the equation px^(2)=log_(e)x has exactly one solution.

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

Find the values of p so that the equation 2cos^2x-(p+3)cosx+2(p-1)=0 has a real solution.

Find the possible values of p such that the equation px^(2)=ln x has exactly one solution.

If cos^(-1)(cosx)=sqrt(1sin2x)AAxepsi(0,2pi), then no. of solution =

Prove that the equation x^(3) + x – 1 = 0 has exactly one real root.