Home
Class 12
MATHS
If sintheta+sinphi=aand costheta+ cosphi...

If `sintheta+sinphi=aand costheta+ cosphi =b,` then

A

(a) `cos((theta-phi)/(2))=+-1/2sqrt(a^(2)+b^(2))`

B

(b) `cos((theta-phi)/(2))=+-sqrt(a^(2)+b^(2))`

C

(c) `tan((theta-phi)/(2))=+-sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))`

D

(d) `cos(theta-phi)=(a^(2)+b^(2)-2)/(2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • EQUATIONS

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

Similar Questions

Explore conceptually related problems

If determinant |cos(theta+phi) sin(theta+phi)cos2phi sin thetacostheta sinphi costheta sintheta cosphi | is a. positive b. independent of theta c. independent of phi d. none of these

If a costheta + b sintheta=3 and a sintheta - b costheta=4 , then a^(2)+b^(2) has the value 25

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

If sintheta+sinphi=sqrt3(cosphi-costheta)) , prove that sin3theta+sin3phi=0

Simplify: cos theta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sin theta ,-costheta),(costheta, sintheta):}]

If sintheta=a/b , then costheta is equal to

Let P = [theta : sintheta – costheta = sqrt2 costheta) andQ= {theta : sintheta + costheta = 12 sintheta} be two sets. Then:

If sintheta+costheta=0 and theta lies in the fourth quadrant, find sintheta and costheta

Statement 1: If A is an orthogonal matrix of order 2, then |A|=+-1. Statement 2: Every two-rowed real orthogonal matrix is of any one of the forms [[costheta ,-sintheta ],[sintheta ,costheta]]or[[costheta ,sintheta],[ sintheta,-costheta]]dot

If sintheta=(1)/(3) , then costheta will be

RESONANCE ENGLISH-DPP-QUESTION
  1. Consider the cubic equation x^(3)-(1+ cos theta+sin theta)x^(2)+(cos t...

    Text Solution

    |

  2. Number of solutions of the equation sin^(4) x-cos^(2)x sin x + 2 sin^(...

    Text Solution

    |

  3. If sintheta+sinphi=aand costheta+ cosphi =b, then

    Text Solution

    |

  4. If sin theta+cos theta=1/5and 0ltthetalt2pi,then tan thetais

    Text Solution

    |

  5. If 0 le x, y le 180^(@) and sin(x-y)=cos (x+y)=1/2, then the values of...

    Text Solution

    |

  6. If tan x + tan 2x + tan 3x = 0 then which of the following can hold go...

    Text Solution

    |

  7. Along a road lies an odd number of stones placed at intervals of 10 m....

    Text Solution

    |

  8. First, second and sevents terms of an A.P. (all the terms are distinct...

    Text Solution

    |

  9. If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to...

    Text Solution

    |

  10. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

    Text Solution

    |

  11. Sum of an infinite G.P. is 5/4 times the sum of all the odd terms. The...

    Text Solution

    |

  12. Sum of an infinitely manu terms of a G.P. is 3 times the sum of even t...

    Text Solution

    |

  13. Given x in (-1,0)uu(0,1)and f(x)= sum(n=0)^(oo) x^(n)(-1)^(n(n+1)/(2))...

    Text Solution

    |

  14. Find the value of cos""(pi)/(12)(sin""(5pi)/(12)+cos""(pi)/(4))+sin"...

    Text Solution

    |

  15. If A and B are two sets, then Ann(bar(AuuB)) is equal to :

    Text Solution

    |

  16. A survey shows that 63% of the people watch a news channel whereas ...

    Text Solution

    |

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

    Text Solution

    |

  18. Two infinite sets have m and n elements. The number of subsets of t...

    Text Solution

    |

  19. In a certain town, 25% families own a phone and 15% own a car, 65% fam...

    Text Solution

    |

  20. If Xuu{1,2}={1,2,3,5,9}, then :

    Text Solution

    |