Home
Class 12
MATHS
If sin^2x-2sinx-1=0 has exactly four dif...

If `sin^2x-2sinx-1=0` has exactly four different solutions in `x in [0,npi]` , then value/values of `n` is/are `(n in N)` 5 (b) 3 (c) 4 (d) 6

A

5

B

3

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
A, C
`sin^(2) x-2 sin x-1=0`
`rArr (sin x-1)^(2)=2` or `sin x-1 = pm sqrt(2)`
or `sin x=1-sqrt(2)` as `sin x cancel(gt) 1`
there are two solutions in `[0, 2pi]` and two more in `[2pi 4pi]`. Thus, `n=4, 5`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercises (Matrix Match Type)|6 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Single)|90 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 x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)

e^(|sinx|)+e^(-|sinx|)+4a=0 will have exactly four different solutions in [0,2pi] if. a in R (b) a in [-3/4,-1/4] a in [(-1-e^2)/(4e),oo] (d) none of these

If 2tan^2x-5secx=1 for exactly seven distinct value of x in [0,(npi)/2],n in N then find the greatest value of ndot

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible values of n is (a)3 (b) 2 (c) 4 (d) 8

If 2tan^2x-5secx=1 is satisfied by exactly seven distinct values of x in [0,((2n+1)pi)/2],n in N , then the greatest value of n is________.

Number of solution(s) satisfying the equation 1/(sinx)-1/(sin2x)=2/(sin4x) in [0,4pi] equals 0 (b) 2 (c) 4 (d) 6

If x=1a n dx=2 are solutions of equations x^3+a x^2+b x+c=0a n da+b=1, then find the value of bdot

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^kdotIfa_1,a_2a n d a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2

The number of values of x in the in interval [0,5pi] satisfying the equation 3sin^2x-7sinx+2=0 is 0 (b) 5 (c) 6 (d) 10

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Multiple)
  1. If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then (a) x=pi/4 (b) y=0 (...

    Text Solution

    |

  2. If 2sin^2((pi/2)cos^2x)=1-cos(pis in2x),x!=(2n+1)pi/2,n in I , then c...

    Text Solution

    |

  3. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |

  4. For the smallest positive values of xa n dy , the equation 2(s inx+s i...

    Text Solution

    |

  5. For the equation 1-2x-x^2=tan^2(x+y)+cot^2(x+y) exactly one value of ...

    Text Solution

    |

  6. If x+y=pi//4 and tan x+tan y=1, then (n in Z)

    Text Solution

    |

  7. If x+y=2pi//3 and sin x//sin y=2, then the

    Text Solution

    |

  8. Let tanx-tan^2x >0 and |2s inx|<1 . Then the intersection of which of ...

    Text Solution

    |

  9. If cos(x+pi/3)+cos x=a has real solutions, then number of integral val...

    Text Solution

    |

  10. If 0lt=xlt=2pi, then 2^cos e c^(2x) sqrt(1/2y^2-y+1)lt=sqrt(2) is sat...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. If (cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0 holds true...

    Text Solution

    |

  13. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

    Text Solution

    |

  14. The value of x in (0,pi/2) satisfying (sqrt(3)-1)/(sinx)+(sqrt(3)+1)/(...

    Text Solution

    |

  15. If cos3theta=cos3alpha, then the value of sintheta can be given by +-s...

    Text Solution

    |

  16. Which of the following sets can be the subset of the general solution ...

    Text Solution

    |

  17. The values of x1 between 0 and 2pi , satisfying the equation cos3x+cos...

    Text Solution

    |

  18. Which of the following set of values of x satisfies the equation 2^(2s...

    Text Solution

    |

  19. If 0 lt x lt 2 pi and |cos x| le sin x, then

    Text Solution

    |

  20. The expression cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin thet...

    Text Solution

    |