Home
Class 12
MATHS
Number of solution of the equation cos^4...

Number of solution of the equation `cos^4 2x+2sin^2 2x=17(cosx+sinx)^8,0

A

4

B

8

C

10

D

16

Text Solution

Verified by Experts

The correct Answer is:
A
Let `sin 2x=y`, then `1+y^(2)=17(1+y)^(4)`
`rArr y= sin 2x=-1//2`
`rArr x=105^(@), 165^(@), 285^(@), 345^(@)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.9|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

The total number of solution of the equation sin^4 x +cos^4 x = sin x cos x in [0,2pi] is :

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

Number of solutions of the equation sin^4x-cos^2xsinx+2sin^2x+sinx=0in0lt=xlt=3pi is_____

Number of solution of equation 2sinx/2cos^2x-2sinx/2sin^2x=cos^2x-sin^2xforx in [0,4pi] is 6 (b) 1 (c) 2 (d) 3

Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x=0 for x in [0, pi] is

The number of solution (s) of the equation sqrt2+cos 2 x=(sin x+cos x) in [-pi/2, pi]

Number of solutions of the equation 4(cos^(2) 2x+ cos 2 x +1)+tan x (tan x-2sqrt(3))=0 in [0, 2pi] is

Find the number of solutions of the equation sinx=x^2+x+1.

The number of solutions of the equation 1+cosx+cos2x+sinx+sin2x+sin3x=0, which satisfy the condition pi/2<|3x-pi/2|lt=pi is

Find the number of solution of the equation 1+e^(cot^2 x )=sqrt(2|sinx|-1)+(1-cos2x)/(1+sin^4x) for x in (0,5pi)dot

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e ...

    Text Solution

    |

  2. The number of solution of sin x+sin 2x+sin 3x =cos x +cos 2x+cos 3x,...

    Text Solution

    |

  3. Number of solution of the equation cos^4 2x+2sin^2 2x=17(cosx+sinx)^8,...

    Text Solution

    |

  4. The number of values of theta in the interval (-pi/2,pi/2) satisfying ...

    Text Solution

    |

  5. The value of k if the equation 2cosx+cos2k x=3 has only one solution i...

    Text Solution

    |

  6. Number of solution(s) satisfying the equation 1/(sinx)-1/(sin2x)=2/(si...

    Text Solution

    |

  7. The number of roots of (1-tan theta) (1+sin 2 theta)=1+tan theta for t...

    Text Solution

    |

  8. If tan(A-B)=1a n dsec(A+B)=2/(sqrt(3)) , then the smallest positive va...

    Text Solution

    |

  9. If 3tan(theta-15^0)=tan(theta+15^0), then theta is equal to n in Z) ...

    Text Solution

    |

  10. If tan 3 theta + tan theta =2 tan 2 theta, then theta is equal to (n i...

    Text Solution

    |

  11. The solution of 4sin^2x+tan^2x+cos e c^2x+cot^2x-6=0i s(n in Z) npi+...

    Text Solution

    |

  12. sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

    Text Solution

    |

  13. The general solution of 4 sin^4 x + cos^4x= 1 is

    Text Solution

    |

  14. For n in Z , the general solution of (sqrt(3)-1)sintheta+(sqrt(3)+1)c...

    Text Solution

    |

  15. The value of cosycos(pi/2-x)-cos(pi/2-y)cosx+sinycos(pi/2-x)+cosxsin(p...

    Text Solution

    |

  16. One of the general solutions of sqrt(3)costheta-3s intheta=4sin2thetac...

    Text Solution

    |

  17. The equation sin^4x+cos^4x+sin2x+alpha=0 is solvable for -5/2lt=alphal...

    Text Solution

    |

  18. The total number of solution of cosx=sqrt(1-sin2x) in [0,2pi] is equal...

    Text Solution

    |

  19. The total number of solution of |cotx|=cotx+1/(sinx),x in [0,3pi] , is...

    Text Solution

    |

  20. Let alphaa n dbeta be any two positive values of x for which 2cosx ,|c...

    Text Solution

    |