Home
Class 11
MATHS
If sinx+siny=sqrt(3)(cos y-cos x), then ...

If `sinx+siny=sqrt(3)(cos y-cos x),` then `sin3x+sin3y=`___________ (a) `2sin3x` (b) 0 (c) 1 (d) none of these

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ \sin x + \sin y = \sqrt{3} (\cos y - \cos x) \] ### Step 1: Use the sum-to-product identities We can express the left-hand side using the sum-to-product identities for sine: ...
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

If sin x+siny=3(cosy-cosx), then the value of (sin3x)/(sin3y), is

If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a) 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

If 2 sin x = sqrt(3) , evaluate (i) 4 sin^(3)x - 3 sin x (ii) 3 cos x - 4 cos^(3)x

(cos^3x-sin^3x)/(cosx-sinx)

If (sinx-cosx)= 0 then find (sin^3 x- cos^3x)

(sin^(3)x)/(1 + cosx) + (cos^(3)x)/(1 - sinx) =

(sin^(3)x)/(1 + cosx) + (cos^(3)x)/(1 - sinx) =

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

If sin^-1 x + sin^-1 y = (2pi)/3, then cos^-1 x + cos^-1 y =

The family of lines (2 cos theta + 3 sin theta) x + (3 cos theta - 5 sin theta) y-(5 cos theta - 2 sin theta) = 0 is concurrent at (x_1, y_1) and the family of lines (a+2b) x+(a-3b) y+b-a=0 for different values of a and b is concurrent at (x_2, y_2) then : (A) x_2 + y_2 = x_1 (B) x_2 + y_2 = y_1 (C) 6x_2 + y_2 = 2x_1 + y_1 (D) none of these

RD SHARMA ENGLISH-TRANSFORMATION FORMULAE-All Questions
  1. Prove that: tantheta.tan(60^0-theta).tan(60^0+theta)=tan3thetadot.'

    Text Solution

    |

  2. Prove that: sin(B-C)cos(A-D) + sin(C-A) cos (B-D) + sin(A-B) cos(C-...

    Text Solution

    |

  3. If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= (a) ...

    Text Solution

    |

  4. Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B...

    Text Solution

    |

  5. Prove that: ((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n={...

    Text Solution

    |

  6. If sintheta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/...

    Text Solution

    |

  7. Prove that: (sin(A-C)+2sinA+sin(A+C)) / ("sin"("B"-"C")+2sinB+"sin"(B+...

    Text Solution

    |

  8. Prove that: ("cos"8Acos5A-cos12 Acos9A)/("sin"8Acos5A+cos12 Asin9A)=ta...

    Text Solution

    |

  9. Prove that: (sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A

    Text Solution

    |

  10. Prove that: 1+cos2x+cos4x+cos6x=4cosxcos2xcos3x

    Text Solution

    |

  11. Prove that: cos18^0-sin18^0 = sqrt(2)sin27^0

    Text Solution

    |

  12. Express each of the following as a product: (i) sin4theta+sin2theta ...

    Text Solution

    |

  13. If (sin(theta+alpha))/(cos(theta-alpha))=(1-m)/(1+m) , prove that tan(...

    Text Solution

    |

  14. If sintheta+sinphi=sqrt3(cosphi-costheta)) , prove that sin3theta+sin...

    Text Solution

    |

  15. Convert each of the following products into the sum or difference of ...

    Text Solution

    |

  16. Convert each of the following products into the sum or difference of ...

    Text Solution

    |

  17. Convert each of the following products into the sum or difference of ...

    Text Solution

    |

  18. Convert each of the following products into the sum or difference of ...

    Text Solution

    |

  19. Convert each of the following products into the sum or difference of ...

    Text Solution

    |

  20. 2cos(pi/13)cos(9pi/13)+cos(3pi/13)+cos(5pi/13)=0

    Text Solution

    |