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

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

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

Find the values of x where function f(X) = (sin x + cosx)(e^(x)) in (0,2pi) has point of inflection

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

Find the number of solution of the equation 2x=3pi (1-cos x) .

Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0,2pi)dot

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

Find the number of integral values of k for which the equation 7 cos x+5 sin x=2k+1 has at least one solution.

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

Find the principal solution of the equation tan x =- (1)/(sqrt3).