Home
Class 12
MATHS
If cos^2x+cosx=a+2, then find the value ...

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

Text Solution

Verified by Experts

The correct Answer is:
[-9/4, 0]
`cos^2x+cosx=a+2`
`rArr (cosx+1/2)^2=a+9/4`
Now, `-1/2lecosx+1/2le3/2`
`:. (cosx+1/2)^2in[0,9/4]`
So, `0lea+9/4le9/4`
`:. -9/4leale0`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|57 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.4|4 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Consider the equation [|x-1|-|x+2|=p. Let rho be the value of rho for which the equationone solution.Also rho_(2) ,is the value of rho for which the equation has infinite solution.Let a be the sum of all the integral values of rho for which this equation has solution rho, is equal to

Find the value of k for which the following system of equation has no solution: x+2y=0,quad 2x+ky=5

Find the value of k for which the following system of equation has no solution: 2x+ky=11,quad 5x-7y=5

Find the value of k for which the following system of equation has no solution: kx-5y=2,quad 6x+2y=7

The number of integral value of k for which the equation 7cos x+5sin x=2k+1 has a solution is

Which of the following equations has x=2 as a solution ?

The set of values of a for which the equation sin^(4)x+cos^(4)x=a has a solution is

Write the set of values of a for which the equation sqrt(3)sin x-cos x=a has no solution.

Find the number of integral values of lambda, for which equation 4cos x+3sin x=2 lambda+1 has a solution.