Home
Class 11
MATHS
Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+...

Prove that: `cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B\ cos C`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA ENGLISH|Exercise All Questions|493 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|120 Videos

Similar Questions

Explore conceptually related problems

In any DeltaABC , prove that : (cos A)/(b cos C + c cos B) + (cos B)/(c cos A + a cos C) + (cos C)/(a cos B + b cos A) = (a^2 + b^2 + c^2)/(2abc)

Prove that: a) sin(A+B+C) + sin(A-B-C)+sin(A+B-C) + sin(A-B+C) = 4sinAcosBcosC b) cos(A+B+C)+cos(A+B-C)+cos(B+C-A)+cos(C+A-B)=4cosAcosBcosC

Prove that: sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-D) = 0

Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B+C)+sin(-A+B+C)+sin(A-B+C)-"sin"(A+B-C))=cot C

Prove that |{:(cos(A-P),cos(A-Q),cos(A-R)),(cos(B-P),cos(B-Q),cos(B-R)),(cos(C-P),cos(C-Q),cos(C-R)):}| =0.

If A+B+C=180^0 , prove that : cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) = 2cos (A/2) cos (B/2) sin (C/2)

In a triangle ABC, prove that: cos^4A+cos^4B+cos^4C= 3/2 + 2 cosA cosB cosC+ 1/2 cos 2A cos2B cos2C

Prove that (cos C + cos A)/(c + a) + (cos B)/(b) = (1)/(b)

Prove that a cos A + b cos B + c cos C = 4 R sin A sin B sin C.

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

RD SHARMA ENGLISH-TRANSFORMATION FORMULAE-All Questions
  1. Prove that: (sin(theta+varphi)-2sintheta+"sin"(theta-varphi))/(cos(the...

    Text Solution

    |

  2. Prove that: sinalpha+sinbeta+singamma-sin(alpha+beta+gamma)=4sin((alph...

    Text Solution

    |

  3. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

    Text Solution

    |

  4. If (cos(A-B))/("cos"(A+B))+("cos"(C+D))/("cos"(C-D))=0,\ prove tht ta...

    Text Solution

    |

  5. If cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta)...

    Text Solution

    |

  6. If (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=lambdacos^2((alpha-beta)/...

    Text Solution

    |

  7. If sin A+sin B=alpha\ a n d\ cos A+cos B=beta, then write the value of...

    Text Solution

    |

  8. If cos A=m cos B , then write the value of cot((A+B)/2)cot((A-B)/2dot)

    Text Solution

    |

  9. Write the value of the expression (1-4sin1 0^0sin7 0^0)/(2sin1 0^0)

    Text Solution

    |

  10. If A+B=pi/3a n dcosA+cos B=1, then find the value of cos((A-B)/2dot)

    Text Solution

    |

  11. Write the value of sin 12^0sin48^0sin54^0dot

    Text Solution

    |

  12. If sin2A=lambdasin2B , then write the value of (lambda+1)/(lambda-1) .

    Text Solution

    |

  13. Write the value of (sin A+sin3A)/(cos A+cos3A) .

    Text Solution

    |

  14. If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a...

    Text Solution

    |

  15. cos 40^0+cos 80^0+cos 160^0+cos 240^0= a. 0 b. 1 c. 1//2 d. -1//2

    Text Solution

    |

  16. sin 163^0cos 347^0+sin 73^0sin 167^0= a.1//2 b. 1 c. 0 d. none of the...

    Text Solution

    |

  17. If sin2theta+sin2varphi=1/2a n d\ cos2theta+cos2varphi=3/2 , then cos^...

    Text Solution

    |

  18. The value of cos 52^0+cos 68^0+cos 172^0 is a. 0 b. 1 c. 2 d. 3//2

    Text Solution

    |

  19. The value of sin 78^0-sin 66^0-sin 42^0+sin6^0 is a. -1 b. 1//2 c. -1/...

    Text Solution

    |

  20. If sinalpha+sinbeta=a\ and\ cosalpha-cosbeta=b , then tan((alpha-beta)...

    Text Solution

    |