Home
Class 11
MATHS
Simplify 2sin^2beta+4cos(alpha+beta)sina...

Simplify `2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)`

Text Solution

Verified by Experts

Given,
`2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)`
we know that,
`cos2(alpha+beta)=2cos^2(alpha+beta)−1`
`=>2sin^2beta+4cos(alpha+beta).sinalphasinbeta+2cos^2(alpha+beta)−1 `
`=2sin^2beta+2cos(alpha+beta)[2sinalphasinbeta+cos(alpha+beta)]−1`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

If cos alpha+cos beta=0=sin alpha+sinbeta, then cos2alpha+cos 2beta=

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. The value of (cot (x/2)-t a n x/2)^2(1-2tanxcot2x) is 1 (b) 2 (c) 3 ...

    Text Solution

    |

  2. Prove that cos^3A+cos^3(120^0+A)+cos^3(240^0+A)=3/4cos3A

    Text Solution

    |

  3. Simplify 2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)

    Text Solution

    |

  4. Prove that: "tan"pi/(16)=sqrt(4+2sqrt(2))-(sqrt(2)+1)

    Text Solution

    |

  5. Prove that tan7 1^circ/2 = sqrt6 - sqrt3 + sqrt2 - 2.

    Text Solution

    |

  6. Prove that:(sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Text Solution

    |

  7. Prove that: (cosA+cosB)^2+(sinA-sinB)^2=4cos^2((A+B)/2) .

    Text Solution

    |

  8. Prove that: (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)=1/8

    Text Solution

    |

  9. If sinA=3/5, where 0^0ltAlt90^0 , then find the values of sin2A , cos2...

    Text Solution

    |

  10. Find the value of sin(pi/10) sin((13pi)/10)

    Text Solution

    |

  11. Show that: sqrt(2+sqrt(2+sqrt(2+2cos8theta)))=2costheta,0<theta<pi 8<=...

    Text Solution

    |

  12. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

    Text Solution

    |

  13. If tan(pi/4+theta/2)=tan^3(pi/4+alpha/2) then sin(theta)=(sin(alpha)(...

    Text Solution

    |

  14. If sin(theta+alpha)=aa n dsin(theta+beta)=b , prove that cos2(alpha-be...

    Text Solution

    |

  15. Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

    Text Solution

    |

  16. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove...

    Text Solution

    |

  17. If costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(th...

    Text Solution

    |

  18. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

    Text Solution

    |

  19. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1) (2cos2thet...

    Text Solution

    |

  20. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

    Text Solution

    |