Home
Class 11
MATHS
By geometrical interpretation, prove tha...

By geometrical interpretation, prove that
(i) `sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha`
(ii) `cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

"Show that :" 2 sin^(2) beta + 4 cos ( alpha + beta) sin alpha sin beta + cos2 (alpha + beta) = cos2 alpha

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (2(1-cos (alpha - beta)))/(cos beta - cos alpha)^(2)=

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

If sin alpha = sin beta and cos alpha = cos beta then-

sin alpha + sin beta = a "and" cos alpha + cos beta = b (tan alpha + tan beta)/(1-tan alpha tan beta)=

Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2) .

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" "tan" (alpha + beta)/2=

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. The equation 2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2la...

    Text Solution

    |

  2. If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >...

    Text Solution

    |

  3. By geometrical interpretation, prove that (i) sin(alpha+beta)=si...

    Text Solution

    |

  4. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

    Text Solution

    |

  5. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a3+x)+ ........+ 1/(2^(n-1)...

    Text Solution

    |

  6. Three circle touch one another externally. The tangents at their point...

    Text Solution

    |

  7. Prove that tan20^0tan40^0tan80^0=tan60^0

    Text Solution

    |

  8. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

    Text Solution

    |

  9. The solution of the system of equations sinxsiny=(sqrt(3))/4,cosxcosy=...

    Text Solution

    |

  10. Find the least value of sec A+secB+secC in an acute angled triangle

    Text Solution

    |

  11. In triangle ABC if cosAcosB +sinAsinB sinC=1 then prove that a:b:c=1:1...

    Text Solution

    |

  12. Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real numbe...

    Text Solution

    |

  13. Number of values of p for which equation sin^3x+1+p^3-3 p sinx=0 (p >0...

    Text Solution

    |

  14. In A B C , prove that cosA+cosB+cosClt=3/2dot

    Text Solution

    |

  15. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

    Text Solution

    |

  16. If pcos e ctheta+qcottheta=2 and p^2cos e c^2theta-q^2cot^2theta=5 t...

    Text Solution

    |

  17. If a, b and c are in G.P. then prove that <math xmlns="http://www.w3...

    Text Solution

    |

  18. In triangle ABC tan(A/2), tan(B/2) and tan (C/2) are in A.P. then prov...

    Text Solution

    |

  19. In triangleABC (b+c)/11=(c+a)/12=(a+b)/13 then prove that (cosA)/7=(co...

    Text Solution

    |

  20. alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, resp...

    Text Solution

    |