Home
Class 12
MATHS
If x +y+z = 180^@, then cos2x + cos2y-...

If `x +y+z = 180^@`, then `cos2x + cos2y-cos2z` is equal to

A

4sinx. siny. sinz

B

1-4sinx.siny.cosz

C

4sinx.siny.sinz-1

D

cosA.cosB.cosC

Text Solution

Verified by Experts

The correct Answer is:
B
`cos2x+cos2y-cos2z`
`=2cos(x+y)cos(x-y)-2cos^(2)z+1`
`=2cos(pi-z)cos(x-y)-2cos^(2)z+1`
`=1-2cosz{cos(x-y)-cos(x+y)}`
`=1-2cosz2sinxsiny`
`=1-4sinxsinycosz`
Promotional Banner

Topper's Solved these Questions

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORER|35 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

Similar Questions

Explore conceptually related problems

2 cos x cos y is equal to:

26. If x,y,z are in A.P,then (sin x-sin z)/(cos z-cos x) is equal to a.tan y b.cot y c.sin y d.cos y

If x,y,z are in A.P.then (sin x-sin z)/(cos z-cos x) is equal to tan y(b)cot y(c)sin y(d)cot y

If x + y = z then cos ^ (2) x + cos ^ (2) y + cos ^ (2) z-2cos x cos y cos z =

If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove that cot (x+y)/2 = cot z and cos (x-y)/2 = pm 1/2

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-FACTORIZATION FORMULAE -EXERCISE 2
  1. The value of cos52^@+cos68^@+cos172^@ is

    Text Solution

    |

  2. The value of sin\ pi/16 sin\ (3pi)/16 sin\ (5pi)/16 sin\ (7pi)/16 is

    Text Solution

    |

  3. The value of cot70^(@)+4cos70^@ is

    Text Solution

    |

  4. 2cos ""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/(13)=0

    Text Solution

    |

  5. If A+B+C=piandsinC+sinAcosB=0, then tanA.cotB is equal to

    Text Solution

    |

  6. If x +y+z = 180^@, then cos2x + cos2y-cos2z is equal to

    Text Solution

    |

  7. If A +B+C= pi and m/C is obtuse then tan A. tan B is

    Text Solution

    |

  8. If A+B+C=180^(@), then (sin2A+sin2B+sin2C)/(cosA+cosB+cosC-1) is equal...

    Text Solution

    |

  9. If A+B+C=270^@ , then cos2A+cos2B+cos2C+4sinAsin B sinC=

    Text Solution

    |

  10. If A, B, C are the angles of a triangle then sin^(2)A+sin^(2)B+sin^(2)...

    Text Solution

    |

  11. If A+B+C=180^(@), then the value of cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2...

    Text Solution

    |

  12. In triangle A B C ,tanA+tanB+tanC=6 and tanAtanB=2, then the values of...

    Text Solution

    |

  13. If a DeltaABC, the value of sinA+sinB+sinC is

    Text Solution

    |

  14. If cosA=cosBcosC and A+B+C=pi, then the value of cotBcotC is

    Text Solution

    |

  15. If sin theta+sin2theta+sin3theta=sin alpha and cos theta+cos 2theta+co...

    Text Solution

    |

  16. tan2 0^0tan4 0^0tan6 0^0tan8 0^0

    Text Solution

    |

  17. sin1 2^(@)sin4 8^(@)sin5 4^(@)=

    Text Solution

    |

  18. If A, B, C, D be the angles of acyclic quadrilateral, show that : cosA...

    Text Solution

    |

  19. If A+B+C=pi, prove that : (cosA)/(sinb sinC) + (cosB)/(sinC sin) + (co...

    Text Solution

    |

  20. If ABCD is a cyclic quadrilateral, then the value of cosA-cosB+cosC-co...

    Text Solution

    |