Home
Class 11
MATHS
Prove that sin^(2)alpha + cos^(2) (alpha...

Prove that `sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin beta cos (alpha + beta)` is independent of `alpha`.

A

`sin^(2) alpha`

B

`sin^(2) beta`

C

`cos^(2)alpha`

D

`cos^(2) beta`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPOUND ANGLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|46 Videos

  • COMPOUND ANGLES

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I)|43 Videos

  • COMPOUND ANGLES

    AAKASH SERIES|Exercise EXERCISE - I|28 Videos

  • CHANGE OF AXES

    AAKASH SERIES|Exercise Practice Exercise|29 Videos

  • CONTINUITY

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS|34 Videos

Similar Questions

Explore conceptually related problems

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

Prove that sin^(2)alpha+cos^(2)(alpha+beta)+2sinalphasinbetacos(alpha+beta) is independent of alpha .

Statement-I : If f(theta)=(cot theta)/(1+cot theta) and alpha+ beta=(5pi)/(4) then f(alpha) f(beta)=(1)/(2) Statement-II : If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then tan alpha= tan beta+ 2tan gamm Statement-III sin^(2) alpha+ cos^(2) (alpha+ beta)+2 sin alpha beta cos (alpha+beta) is independent of alpha only

sin alpha=sinbeta, cos alpha=cos beta then

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

If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

Prove that cos^(2)(alpha-beta)+cos^(2)beta-2cos(alpha-beta)cosalphacosbeta is independent of beta .

If cos alpha+cos beta=0=sin alpha+sin beta , then cos 2 alpha+cos 2beta is equal to

If sin alpha + sin beta = a , cos alpha + cos beta = b " then cos ( alpha + beta ) =

AAKASH SERIES-COMPOUND ANGLES-EXERCISE - II
  1. If Cot A Cot B = 2 & Cos (A+B) = 3/5 then Sin A Sin B

    Text Solution

    |

  2. If cos (A-B)=3//5 and tan A tan B=2 , then which one of the following...

    Text Solution

    |

  3. Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin bet...

    Text Solution

    |

  4. sin A + sin B = sqrt(3) ( cos B- cos A )implies sin 3A + sin 3B=

    Text Solution

    |

  5. If (CosA)/(CosB)=nand(SinA)/(SinB)=m then (m^(2) - n^(2)) Sin^(2) B =

    Text Solution

    |

  6. If tan A=(x sin B)/(1- x cos B) and tan B=(y sin A)/(1-y cos A) then ...

    Text Solution

    |

  7. If tan beta =(n tan alpha )/(1+(1-n) tan^(2) alpha ), then tan(alpha-...

    Text Solution

    |

  8. If sin (120^(@) - alpha) = sin (120^(@) - beta) and 0 lt alpha,beta lt...

    Text Solution

    |

  9. If 2 tan A + cot A = tan B , then cot A +2 tan (A-B)=

    Text Solution

    |

  10. In a Delta ABC , if the angle C is obtuse, then tan A ta B =

    Text Solution

    |

  11. In a triangle ABC, fi Tan A + Tan B + Tan C = 6 and Tan A Tan B = 2 th...

    Text Solution

    |

  12. In Dleta ABC if Tan B = (2Sin ASinC)/(Sin(A+C)) then TanA, TanB, TanC ...

    Text Solution

    |

  13. In a triangle ABC, If cot A+ cotB +cot C=sqrt3, then show that the tri...

    Text Solution

    |

  14. Tan A + Tan B + Tan C - (sin(A+B+C))/(cosAcosBcosC)=

    Text Solution

    |

  15. Statement-I : If 0 lt alpha, beta lt pi/4, sin alpha =a/sqrt(1+a^(2)),...

    Text Solution

    |

  16. I : If x cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@)...

    Text Solution

    |

  17. A =(cos 9^(@) - sin 9^(@))/(cos 9^(@) + sin 9^(@)) , B = (cos 21^(@) +...

    Text Solution

    |

  18. Assertion (A) : If cos(x-y) = 3 cos (x + y) then cotx cotx = 2 Reaso...

    Text Solution

    |

  19. Assertion (A) : tan (alpha - beta) + tan (beta - lambda) + tan (lambda...

    Text Solution

    |

  20. Assertion (A) : tan 70^(@) - tan 20^(@) = 2 cot 40^(@) Reason (R ) : I...

    Text Solution

    |