Find the value of `a` for which the equation a `sin(x+pi/4)=sin2x+9` will have real solution.

Find the values of a for whilch the equation sin^4x+asin^2x+1=0 will have a solution.

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 all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

The set of values of k for which the equation sin^(-1)x+cos^(-1)x +pi(|x|-2)=k pi possesses real solution is [a,b] then the value of a + b is

Find the values of a for which the equation ||x-2|+a|=4 can have four distinct real solutions.

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

The range of 'y, such that the equation in x, y + cos x = sin x has a real solution is

For which values of a does the equation 4sin(x+pi/3)cos(x-pi/6)=a^2+sqrt(3)sin2x-cos2x have solution? Find the solution for a=0 , if any exists

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 value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))