Home
Class 11
MATHS
Prove that : cos^2alpha+cos^2(alpha+beta...

Prove that : `cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta`

Text Solution

Verified by Experts

Given,
`cos^2alpha+cos^2(alpha+beta)−2cosalphacosbetacos(alpha+beta)`
`⇒cos^2alpha+cos(alpha+beta)[cos(alpha+beta)−2cosalphacosbeta]`
`=>cos^2alpha+cos(alpha+beta)[cosalphacosbeta−sinalphasinbeta−2cosalphacosbeta]`
`⇒cos^2alpha+cos(alpha+beta)[cosalphacosbeta−sinalphasinbeta−2cosalphacosbeta]`
`⇒cos^2alpha−cos(alpha+beta) [sinalphasinbeta+cosalphacosbeta]`
`⇒cos^2alpha−cos(alpha+beta)cos(alpha−beta)`
...
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA|Exercise Solved Examples And Exercises|181 Videos

Similar Questions

Explore conceptually related problems

Prove that: cos ^ (2) alpha + cos ^ (2) (alpha + beta) -2cos alpha cos beta cos (alpha + beta) = sin ^ (2) beta

If A = cos ^(2) alpha + cos ^2(alpha + beta)- 2 cos alpha cos beta cos (alpha + beta), then

underset is f(alpha. beta)=cos^(2)+beta cos^(2)(alpha+beta)-2cos alpha cos beta cos(alpha+beta)

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=

Prove,by induction,that sin alpha+cos(alpha+beta)-sin(alpha+2 beta)-cos(alpha+3 beta)+sin(alpha+4 beta)+... to n terms

Prove that : (cos alpha+cos beta)^(2)+(sin alpha+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

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

RD SHARMA-MATHEMATICAL INDUCTION-Solved Examples And Exercises
  1. Prove by the principle of mathematical induction that: n(n+1)(2n+1) is...

    Text Solution

    |

  2. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  3. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

    Text Solution

    |

  4. Prove that 1/(n+1)+1/(n+2)+...+1/(2n)> 13/24 ,for all natural number ...

    Text Solution

    |

  5. Prove the following by using the principle of mathematical inductio...

    Text Solution

    |

  6. Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is pos...

    Text Solution

    |

  7. If P(n) is the statement n^3+n is divisible 3 is the statement P(3) tr...

    Text Solution

    |

  8. If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the...

    Text Solution

    |

  9. Let P(n) be the statement 7 divides (2^(3n)-1)dot What is P(n+1)?

    Text Solution

    |

  10. If P(n) is the statement n(n+1), then what is P(3)?

    Text Solution

    |

  11. If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is t...

    Text Solution

    |

  12. If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1...

    Text Solution

    |

  13. If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(...

    Text Solution

    |

  14. Given an example of a statement P(n) such that it is true of all n inN...

    Text Solution

    |

  15. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2) and...

    Text Solution

    |

  16. Given an example of a statement P(n) which is true for all ngeq4 but P...

    Text Solution

    |

  17. Prove by the principle of mathematical induction that for all n N ...

    Text Solution

    |

  18. Using principle of mathematical induction prove that x^(2n)-y^(2n) i...

    Text Solution

    |

  19. Prove by the principle of induction that for all n N ,\ (10^(2n-1)+1)...

    Text Solution

    |

  20. Prove by induction that 4+8+12++4n=2n(n+1) for all n Ndot

    Text Solution

    |