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

The range of the values of p for which the equation sin cos^(-1) ( cos (tan^(-1) x)) = p has a solution is

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

Find the values of k so that the equation x^(2)-2x(1+3k)+7(3+2k)=0 has real and equal roots.

For what value of k the equation sinx+cos(k+x)+cos(k-x)=2 has real solutions?

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

Find the set of real value(s) of a for which the equation |2x+3|+|2x-3|=a x+6 has more than two solutions.

Find the value of alpha and p if the equation xcosalpha+ysinalpha=p is the normal form of the line sqrt(3x)+y+2=0 .