Home
Class 12
MATHS
If 3sinx+4cosa x=7 has at least one solu...

If `3sinx+4cosa x=7` has at least one solution, then find the possible values of `adot`

Text Solution

Verified by Experts

We have `3 sin x+4 cos ax=7` which is possible only when
`sin x=1` and `cos ax =1`
or `x=(4n+1) pi/2` and `ax=2mpi, m, n in Z`
or `(4n+1) pi/2=(2m pi)/a`
or `a=(4m)/(4n+1), m, n in Z`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.1|12 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.2|6 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, then the sum of all possible integral values of a is equal to

If f(x)=sgn(2sinx+a) is continuous for all x , then find the possible values of adot

If the equation asinx+cos2x=2a-7 possesses a solution, then find the value of adot

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

If the roots of the equation x^2-8x+a^2-6a=0 are real and distinct, then find all possible value of adot

Consider the inequality, 9^(x)-a.3^(x)-a+3 le 0 , where 'a' is a real parameter. (a) Find the value of 'a' for which the inequality has at least one negative solution. (b) Find the values of 'a' for which the inequality has at least one positive solution. (c) Find the vlaues of 'a' for which the inequality has at least one real solution.

If x^2+2a x+a<0AAx in [1,3], the find the values of adot

If the equation z^3 + (3 + l)(z^2) - 3z - (m + l)= 0, m in R , has at least one real root, then sum of possible values of m, is

If 2cosx+sinx=1, then find the value of 7cosx+6sinxdot

If x^(4) + 2kx^(3) + x^(2) + 2kx + 1 = 0 has exactly tow distinct positive and two distinct negative roots, then find the possible real values of k.