Home
Class 12
MATHS
If p=sin(A-B)sin(C-D),q=sin(B-C)sin(A-D)...

If `p=sin(A-B)sin(C-D),q=sin(B-C)sin(A-D),r=sin(C-A)sin(B-D)` then `p+q-r=0` (b) `p+q+r=0` `p-q+r=0` (d) `p^3+q^3+r^3=3p q r`

A

`p+q-r=0`

B

`p+q+r=0`

C

`p-q+r=0`

D

`p^(3)+q^(3)+r^(3)=3pqr`

Text Solution

Verified by Experts

The correct Answer is:
B, D
` 2p = cos ( A-B -C +D) - cos (A -B + C-D)`
`rArr " " 2q = cos (B-C-A +D)-cos(B-C +A-D)`
`rArr " "2r = cos(C -A -B +D) -cos (C-A +B-D)`
`rArr " " 2p + 2q + 2r = 0`
`" " p+q + r =0 and p^(3) +q^(3) +r^(3)= 3pqr`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Matrix Match Type )|9 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Single)|100 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If =sin(A-B)sin(C-D),q=sin(B-C)sin(A-D)p=sin(C-B)sin(B-D) then (a)p+q-r=0 (b) p+q+r=0p-q+r=0(d)p^(3)+q^(3)+r^(3)=3pqr

If sin(A+B)=p,cos^(2)(A+C)=q, where q>0 then sin(B-C)=

|[sin(x+p),sin(x+q),sin(x+r)],[sin(y+p),sin(y+q),sin(y+r)],[sin(z+p),sin(z+q),sin(z+r)]| =

If P+Q+R=180^(@) then the value of psi n(Q-R)+q sin(R-P)+r sin(P-Q)

The lines (p-q)x+(q-r)y+(r-p)=0(q-r)x+(r-p)y+(p-q)=0,(x-p)x+(p-q)y+(q-r)=

If (x+2) is a common factor of (px^(2)+qx+r) and (qx^(2)+px+r) then a p=q or p+q+r=0 b p=r or p+q+r=0 c) q=r or p+q+r=0 d p=q=-(1)/(2)r

If in a triangle PQR;sin P,sin Q,sin R are in A.P; then

If a=xy^(p-1),b=yz^(q-1),c=zx^(r-1) , then a^(q-r)b^(r-p)c^(p-q) is equal to

If in a Delta PQR , sin P, sin Q , sin R are in AP, then:

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Multiple)
  1. Which of the following quantities are rational? sin((11pi)/(12))sin((5...

    Text Solution

    |

  2. In which of the following sets the inequality sin^6x+cos^6x >5/8 holds...

    Text Solution

    |

  3. Let f(x)=x^(2)-2sqrt((sinsqrt(3)-sinsqrt(2)))x-(cossqrt(3)-cos sqrt(2)...

    Text Solution

    |

  4. For alpha=pi/7 which of the following hold (s) good?

    Text Solution

    |

  5. Which of the following identieis, wherever defined, hold(s) good?

    Text Solution

    |

  6. The expression (tan^4x+2tan^2x+1)cos^2x ,w h e nx=pi/(12), can be equa...

    Text Solution

    |

  7. Let alpha,betaa n dgamma be some angles in the first quadrant satisfyi...

    Text Solution

    |

  8. Let fn(theta)=(cos theta/2+cos 2theta + cos (7theta)/2+...+cos (3n-2) ...

    Text Solution

    |

  9. If sin(x+20^0)=2sinxcos40^0,w h r ex in (0,pi/2), then which of the fo...

    Text Solution

    |

  10. The expression cos^2(alpha+beta)+cos^2(alpha-beta)-cos2alphacos2beta i...

    Text Solution

    |

  11. If cot^3 alpha+ cot^2 alpha + cot alpha=1 then which of the following ...

    Text Solution

    |

  12. If p=sin(A-B)sin(C-D),q=sin(B-C)sin(A-D),r=sin(C-A)sin(B-D) then p+q-r...

    Text Solution

    |

  13. If cosx-sinalphacotbetasinx=cosa , then the value of tan(x/2) is -tan(...

    Text Solution

    |

  14. Let f(x)=ab sin x+bsqrt(1-a^(2))cosx+c, where |a|lt1,bgt0 then

    Text Solution

    |

  15. Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)/(4k)) (1+cos((2k+1)pi)/(4k))...

    Text Solution

    |

  16. If 3 sin beta=sin(2alpha+beta), then tan (alpha+beta)-2 tan alpha is

    Text Solution

    |

  17. x=sqrt(a^2cos^2alpha+b^2sin^2alpha)+sqrt(a^2sin^2alpha+b^2cos^2alpha) ...

    Text Solution

    |

  18. If (x-a)costheta+ysintheta=(x-a)cosvarphi+ysintheta=aa n dtan(theta/2)...

    Text Solution

    |

  19. If cos (x-y),, cosx and cos(x+y) are in H.P., are in H.P., then cosx*s...

    Text Solution

    |

  20. Difference between maximum and minimum values of (60sin alpha+p cos al...

    Text Solution

    |