`3cosx+4Sinx = k+1` then set of integral value of k

If there are infinite values of x satisfying |x-3|-|x+4|=k then possible number of integral values of k is/are

Find the number of integral values of k for which the equation 12cosx - 5 sinx = 2k+1 has a solution.

If the solution set of |x-k|<2 is a subset of the solution set of the inequality (2x-1)/(x+2)<1 then the number of possible integral value(s) of 'k' is/are-

If int_(0)^(pi/2)(dx)/(3cosx + 5) = k cot^(-1) 2 , then what is the value of K ?

If 3sinx+4cosx=2 , then find the value of 3cosx-4sinx .

Consider the integrals I=int(sinx)/(3cos x+4sinx)dx and J=int(cosx)/(3cos x+4sinx)dx . Then, the integral 4J-3J is equal to (where, c is the constant of integration)

If (sinx)/(1+cosx)+(sinx)/(1-cosx)=4 and 0^@ le x le 90^@ , then the value of x is

If polynomials P and Q satisfy int[(3x-1)cosx+(1-2x)sinx ]dx=P cosx+Qsinx (ignore the constant of integration) then :