Find the value of `x` for which `3cosx=x^2-8x+19` holds good.

Find the value of x for which cos e c^(-1)(cosx) is defined.

If cos^2x+cosx=a+2 , then find the value of a for which equation has solution.

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

Find the set of value of x for which the equation cos^(-1) x + cos^(-1) ((x)/(2) + (1)/(2) sqrt(3 -3x^(2))) = (pi)/(3) holds goods

Find the integral value of n for which lim_(x->0)(cos^2x-cosx-e^xcosx+e^x-(x^3)/2)/(x^n) is a finite nonzero number

Find all value of x for which (x^(3)(x-1))/((x-2))gt 0

Find the values of a for which all the roots of the equation x^4-4x^3-8x^2+a=0 are real.

Find the values of a for which the roots of the equation x^2+a^2=8x+6a are real.

Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6. Find the remaining factor for this value of pdot