Home
Class 12
MATHS
If sin^(4) alpha + 4 cos^(4) beta + 2 = ...

If `sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi]`, then `cos (alpha + beta) - cos (alpha - beta)` is equal to `-sqrt(k)`. The value of k is _________.

A

`-sqrt(2)`

B

`0`

C

`sqrt(2)`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

Similar Questions

Explore conceptually related problems

If sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(2) , then (sin alpha+cos beta) is equal to

If cos(alpha+beta)=0 then sin(alpha+2beta)=

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/2) is equal to-

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

If alpha+beta= 60^0 , prove that cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4 .

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If sin alpha + sin beta=a and cos alpha+cosbeta=b then tan((alpha-beta)/2) is equal to

If cos(alpha + beta)=0 , then sin (alpha-beta) can be reduced to

RESONANCE ENGLISH-FUNDAMENTAL OF MATHEMATICS-Exercise
  1. If A=sin^(2)x+cos^(4)x, then for all real x

    Text Solution

    |

  2. Let X""=""{1,""2,""3,""4,""5} . The number of different ordered pairs ...

    Text Solution

    |

  3. In a Delta PQR , if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1, th...

    Text Solution

    |

  4. Let A and B be two sets containing 2 elements and 4 elements, respecti...

    Text Solution

    |

  5. The expression (tan A)/(1-cotA)+(cot A)/(1-tan A) can be written as

    Text Solution

    |

  6. If X={4^(n)-3n-1:ninN}andy={9(n-1):ninN}, then X uu Y equals

    Text Solution

    |

  7. Let fk(x)=1/k(sin^kx+cos^kx)" where "x in R and kge1. " Then "f4(x) -f...

    Text Solution

    |

  8. Let A and B be two sets containing 2 elements and 4 elements, respecti...

    Text Solution

    |

  9. If the anlges of elevation of the top of a tower from three collinear ...

    Text Solution

    |

  10. If 0 le x le 2pi, then the number of real values of x, which satisfy t...

    Text Solution

    |

  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

    Text Solution

    |

  12. Let a vertical tower A B have its end A on the level ground. Let C be ...

    Text Solution

    |

  13. Let S= {x in R : x ge 0 and 2 |sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) +...

    Text Solution

    |

  14. If the sum of all the solutions of the equation 8 cosx.(cos(pi/6+x)cos...

    Text Solution

    |

  15. PQR is a triangular park with PQ=PR=200m. A.T.V. tower stands at the m...

    Text Solution

    |

  16. Let S= {x in R : x ge 0 and 2 |sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) +...

    Text Solution

    |

  17. In a class of 140 students numbered 1 to 140, all even numbered studen...

    Text Solution

    |

  18. The sum of all values of theta in (0,pi/2) satisfying sin^(2)2theta+co...

    Text Solution

    |

  19. the value of cos((pi)/(2^2))cos((pi)/(2^3))cos((pi)/(2^4)) .....cos((...

    Text Solution

    |

  20. If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, a...

    Text Solution

    |